^ I Ct<c«.A  p"  * 


OIMaW.. 


DUKE 

UNIVERSITY 


LIBRARY 


w ' V' 


A A A 

— I 

A & £- 

xE  . 12: 

A 1 l 

-1 , Hr 

Add 

JL 

& At  £• 

I . JL 

[ A ( 

—on.  lx . 

oho 

— - I , nr 

& I 0 

i.n.  n 

A A | 

G THE  v Tv 

GAO 

— TH- . T7- 

Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/logicdeductivein01hibb 


LOGIC 


DEDUCTIVE  AND  INDUCTIVE 


BOOKS  BY  JOHN  GRIER  HIBBEN,  Ph.D. 
PUBLISHED  BY  CHARLES  SCRIBNER’S  SONS 


LOGIC,  DEDUCTIVE  AND  INDUCTIVE, 

net  $1.40 

THE  PROBLEMS  OF  PHILOSOPHY  . net  1.00 

HEGEL’S  LOGIC net  1.25 

INDUCTIVE  LOGIC 1.50 


LOGIC 


DEDUCTIVE  AND  INDUCTIVE 


BY 

JOHN  GRIER  HIBBEN,  Ph.D. 

STUART  PROFESSOR  OF  LOGIC  IN  PRINCETON  UNIVERSITY 


NEW  YORK 

CHARLES  SCRIBNER’S  SONS 
1906 


COPYRIGHT,  1896,  1905,  BY 
CHARLES  SCRIBNER'S  SONS 


Nortoooh  ftrras 

J.  S.  Cushing  & Co.  — Berwick  & Smith  Co. 
Norwood,  Mass.,  U.S.A, 


I lei 


2Ea 

JOHN  DAVIDSON 

IN  APPRECIATION  OF  THE  VALUABLE  SUGGESTIONS 
RECEIVED  IN  THE  PREPARATION  OF  THIS  BOOK, 
AND  OF  THE  KINDLY  INTEREST  EXPRESSED 
IN  MANY  WAYS  THROUGH  YEARS  OF 
AN  INTIMATE  FRIENDSHIP 


“O  fxiv  yap  <Tuv07rrtK05  SiaAe/m/cos,  6 8e  ou. 

— Plato  : Republic  VII,  537  C. 


PREFACE 


This  book  consists  of  two  parts,  — the  Deductive  and 
the  Inductive  Logic.  The  former  treats  of  the  general 
nature  of  our  thought  processes  as  well  as  the  fundamental 
principles  and  practice  of  deduction,  and  is  now  published 
for  the  first  time.  The  latter  is  my  Inductive  Logic  which 
was  published  in  1896,  now  revised  and  incorporated  in 
this  volume.  It  has  been  my  endeavor  to  present  in  con- 
nection with  the  more  formal  and  traditional  treatment  of 
the  deductive  logic  also  some  considerations  which  have 
been  contributed  by  the  discussions  of  the  modern  logic 
and  which  find  expression  in  such  works  as  those  of  Sig- 
wart,  Lotze,  Erdmann,  Green,  Bosanquet,  Venn,  and  others. 

The  illustrations  and  examples  contained  in  the  text  are 
taken  as  far  as  possible  from  the  sphere  of  everyday  expe- 
riences, in  order  that  they  may  represent  modes  of  actual 
reasoning  pursued  by  the  common  run  of  mankind.  With 
this  end  in  view,  all  the  stock  examples  which  have  grown 
old  and  infirm  in  the  service  of  many  generations  of  stu- 
dents in  logic  have  been  omitted.  Moreover,  the  material 
as  well  as  the  formal  significance  of  the  judgments  em- 
ployed in  reasoning  has  been  emphasized  in  order  that  the 
student  may  come  to  regard  logic  as  a living  process  of 
thought  functioning  in  a normal  and  natural  manner,  and 
not  as  an  artificial  manipulation  of  certain  dead  elements 
mechanically  adjusted  one  to  another. 

The  illustrations  which  appear  in  the  Inductive  Logic, 
and  which  are  taken  from  the  experiments  of  Faraday, 
Tyndall,  Darwin,  Pasteur,  Lubbock,  and  others,  are  quoted 

vii 


PREFACE 


viii 


for  the  most  part  at  considerable  length,  not  merely  be- 
cause in  the  concrete  case  the  universal  principles  of  rea- 
soning and  of  method  are  often  most  forcibly  discovered, 
but  also  because  the  experiments  of  such  pioneers  in  re- 
search actually  create  these  methods  of  investigation,  or 
at  least  serve  to  render  them  exact  and  definite. 

In  Chapter  XIV,  Part  I,  “ A Generalization  of  Immediate 
Inferences,”  I have  presented  some  original  material,  — this 
being  an  attempt  on  my  part  to  summarize  all  the  possible 
transformations  of  any  given  proposition  according  to  a 
scheme  suggested  by  the  Aristotelian  square  of  opposition, 
and  developed  along  similar  lines.  In  addition  to  the 
general  field  usually  covered  by  writers  on  deductive  logic, 
there  is  appended  a discussion  on  “ Extra-syllogistic  Reason- 
ing,” being  Chapter  XVIII,  Part  I. 

I wish  to  avail  myself  of  this  opportunity  to  express  my 
appreciation  of  the  suggestions  and  help  which  I received 
from  my  colleagues,  Dean  Andrew  F.  West  and  Professor 
Winthrop  M.  Daniels,  in  the  preparation  of  the  Logical 
Exercises  which  appear  at  the  end  of  Part  II. 


Princeton,  N.J., 
December  23,  1904. 


J.  G.  H. 


CONTENTS 


PART  I 

DEDUCTIVE  LOGIC 

CHAPTER  I 

PAGE 

The  Nature  of  Thought 3 

Definition  and  nature  of  Logic,  3.  Thought  as  reflection,  4. 

The  four  functions  of  thought,  4.  Concept,  judgment,  in- 
ference, 10.  Logic  as  a normative  science,  11. 


CHAPTER  II 

The  Concept 13 

Relation  of  identity  to  diversity  in  concepts,  13.  The 


natural  history  of  the  concept,  15.  Logical  and  empirical 
concepts,  16.  Genetic  concepts,  22.  Thought  and  lan- 
guage, 23. 

CHAPTER  III 

The  Judgment 25 

The  essential  nature  of  judgment,  25.  Universal  and 
singular  judgments,  26.  Relation  of  judgment  to  reality, 

27.  The  element  of  necessity  in  judgment,  30.  The  uni- 
versal element  in  judgment,  31.  Judgment  and  language, 

33.  Subject,  predicate,  and  copula,  33. 

CHAPTER  IV 

The  Universal  Judgment 36 

The  categories  of  Aristotle,  37.  Heads  of  Predicables,  38. 
Various  types  of  judgment,  40.  Extension  and  intension, 
denotation  and  connotation,  42. 


IX 


X 


CONTENTS 


CHAPTER  V 

PAGE 

Definition  . 44 

Nature  of  definition,  44.  Real  and  nominal  definition,  44. 

Rules  of  definition,  45.  Definition  by  description,  47. 
Definition  for  purpose  of  identification,  48.  Genetic  defi- 
nition, 48. 


CHAPTER  VI 

Division  and  Classification 50 

Nature  of  division,  50.  Rules  of  division,  51.  Dichotomy, 

61.  Contrary  and  contradictory,  52.  Trichotomy,  53. 
Empirical  and  logical  divisions,  54.  Nature  of  classifica- 
tion, 55.  Artificial  and  natural  classification,  56.  Serial 
classification,  58.  Effect  of  the  doctrine  of  evolution  on 
theory  of  classification,  59.  Classification  of  the  sciences, 

61.  Classifications  of  Bacon,  Comte,  and  Spencer,  62. 

CHAPTER  VII 

The  Singular  Judgment 67 

Its  relation  to  the  universal  judgment,  67.  Impersonal, 
perceptive,  and  demonstrative  judgments,  67.  Determinate 
reference,  68.  Indeterminate  reference,  69.  Judgment 
concerning  a proper  name,  69. 

CHAPTER  VIII 

The  Negative  Judgment  .......  73 

Nature  of  the  negative  judgment,  73.  Its  function  of 
exact  determination,  74.  Its  positive  ground,  75.  Signifi- 
cant negation,  75.  Implication  in  negation,  76.  Infinite 
negation,  77. 

CHAPTER  IX 

The  Categorical,  Hypothetical,  and  Disjunctive 

Judgments 78 

The  nature  of  each,  78.  Their  relation  to  universal  and 
singular  judgments,  79.  Their  relation  to  the  progressive 
stages  of  knowledge,  81.  Modality  of  judgments,  83. 


CONTENTS 


XI 


CHAPTER  X 

PAGE 

The  Nature  of  Inference 85 

Logical  and  psychological  elements  in  inference,  85.  Ob- 
jective and  subjective  necessity,  87.  Data  of  perception, 

88.  System  as  ground  of  inference,  89.  The  implicit  and 
explicit,  92.  Inference  mediated  through  the  universal,  93. 
Conceptual  processes,  94.  Explanation,  94.  Relation  of 
inference  to  judgment,  95. 

CHAPTER  XI 

The  Laws  of  Thought 98 

The  law  of  identity,  98.  The  law  of  contradiction,  100. 

The  law  of  excluded  middle,  101.  The  law  of  sufficient 
reason,  102. 


CHAPTER  XII 

Immediate  Inference 103 

Immediate  inference,  a misnomer,  103.  The  processes  of 
implication  and  transformation,  103.  The  square  of  opposi- 
tion, 104.  Practical  suggestions  based  on  opposition,  108. 

CHAPTER  XIII 

On  Transformations  of  Judgment  Forms  . . .110 

Conversion,  110.  Content  and  form  in  conversion,  113. 
Obversion,  114.  Contraposition,  114. 

CHAPTER  XIV 

A Generalization  of  Immediate  Inferences  . . 117 

Summary  of  possible  transformations,  117.  The  A square, 

118.  The  E square,  119.  The  I square,  120.  The  O 
square,  120. 

CHAPTER  XV 

Mediate  Inference  — The  Syllogism  ....  122 
Structure  and  functions  of  the  syllogism,  122.  Distribu- 
tion of  terms,  125.  Rules  for  criticism  of  validity  of  syllo- 


CONTENTS 


xii 


PAGE 

gisms,  126.  Modification  of  these  rules  in  special  cases,  129. 
Enthymeme,  130.  Prosyllogism,  episyllogism,  and  the 
sorites,  132. 

CHAPTER  XVI 

Mood  and  Figure 134 

The  valid  moods,  134.  Figure,  137.  Mnemonic  lines, 

139.  Reduction,  140. 

CHAPTER  XVII 

The  Hypothetical  and  Disjunctive  Syllogisms  . . 142 

Hypothetical  syllogism,  142.  Disjunctive  syllogism,  146. 
Dilemma,  145.  Trilemma,  148. 


CHAPTER  XVIII 

Extra-syllogistic  Reasoning  ......  149 

Reasoning  from  particulars  to  particulars,  149.  The  typi- 
cal case  a disguised  universal,  151.  Inference  based  upon 
given  relations,  152.  Its  relation  to  the  underlying  system, 

154.  The  logic  of  relatives,  156. 

CHAPTER  XIX 


Fallacies 157 

Formal  fallacies,  167.  Material  fallacies,  158.  Equivo- 
cation, 158.  Amphiboly,  159.  Composition,  159.  Divi- 
sion, 160.  Accent,  160.  Figure  of  speech,  160.  Accident, 

161.  Converse  accident,  161.  Ignoratio  Elenchi,  162.  Non 
sequitur,  164.  Petitio  Principii , 164.  Non  causa  pro 
causa,  165.  Many  questions,  165. 


CONTENTS 


xiii 


PART  II 

INDUCTIVE  LOGIC 

CHAPTER  I 

PAGE 

Induction  and  Deduction 169 

Various  opinions  concerning  their  relative  importance, 

169.  Regarded  as  different  phases  of  one  and  same  pro- 
cess, 170.  Their  relation  to  the  ground  of  inference  as 
system,  170.  Their  relation  to  the  universal,  171.  Truth 
and  fact,  171.  Mutual  dependence  of  deduction  and  induc- 
tion, 172. 


CHAPTER  II 

The  Essentials  of  Induction 175 

The  inductive  hazard,  175.  Basal  postulate  of  induction, 

176.  Its  epistemological  nature,  177.  Reduction,  177. 

Law  and  rule,  180.  Law  as  a hypothetical  universal, 

181.  Induction  in  practical  affairs  of  life,  181.  Scientific 
spirit,  182. 


CHAPTER  III 

Types  of  Inductive  Inference 183 

Method  of  enunciation,  183.  (a)  Perfect  induction,  184. 

( b ) Incomplete  induction,  186.  (c)  Probability,  186. 

Method  of  Analogy,  187.  Method  of  Scientific  Analysis, 

188.  The  causal  element  in  these  various  methods,  189. 


CHAPTER  IV 

Causation 195 

Phenomenal  significance  of  causal  concept,  196.  Philo- 
sophical significance,  197.  Logical  significance,  198.  Origin 
of  belief  in  uniformity  of  nature,  199.  Popular  and  scien- 
tific idea  of  cause,  201.  Causal  analysis,  202.  Limitations 
of  knowledge,  203. 


XIV 


CONTENTS 


CHAPTER  V 

PAGE 

The  Method  of  Causal  Analysis  and  Determination  206 
Sequence,  206.  Concurrence,  207.  Coexistence,  208. 
Collocations,  209.  Transfer  of  energy,  211.  Quantitative 
determination,  211.  Observation  and  experiment,  213. 
Negative  determination,  217.  Pseudo-causal  connections, 

219. 

CHAPTER  VI 

Mill’s  Inductive  Methods  — The  Method  of  Agree- 
ment   222 

The  five  methods,  222.  Agreement,  224.  Symbolical 
representation,  225.  Variation  of  instances,  227.  Obser- 
vation, 228.  Simple  enumeration,  228.  Sequence  and 
coexistence,  229.  Criticism  of  this  method,  229.  Agree- 
ment as  a method  of  suggestion,  232.  Illustrations,  232. 

CHAPTER  VII 

The  Method  of  Difference 236 

Its  relation  to  agreement,  236.  Its  characteristic  features, 

236.  Symbolical  representation,  238.  Relation  to  negative 
determination,  239.  Difference  and  combinations,  239. 
Criticism  of  the  method,  240.  Practical  difficulties,  242. 
Illustrations,  245.  Blind  experiments,  247. 

CHAPTER  VIII 

The  Joint  Method  of  Agreement  and  Difference  . 248 
Relation  to  method  of  difference,  248.  Its  characteristics 
and  symbolical  representation,  249.  Illustrations,  250. 
Advantages  of  this  method,  257. 

CHAPTER  IX 

The  Method  of  Concomitant  Variations  . . . 258 

Characteristics  and  symbolical  representation,  258.  Quan- 
titative determination,  259.  Graphical  representation,  260. 
Advantages  in  its  psychological  impressions,  261.  Illustra- 
tions, 262.  Comprehension  of  unknown  forces  by  this 
method,  266.  Precautions  in  using  this  method,  267. 


CONTENTS 


XV 


CHAPTER  X 

PAGH 

The  Method  of  Residues  . 271 

Characteristics  and  symbolical  representation,  271.  A 
deductive  method,  272.  Its  function  suggestive,  273.  Illus- 
trations, 273.  Its  practical  value,  277. 


CHAPTER  XI 

Prediction  and  Verification  ......  278 

The  inducto-deductive  method,  278.  Illustrations,  279. 
Bacon’s  anticipations  of  nature,  283.  Scientific  thought, 

284.  Indirect  method  of  prediction,  286.  Exceptional 
phenomena,  288,  Generalization,  289.  Mathematical 
method,  290. 

CHAPTER  XII 

Hypothesis 291 

Its  relation  to  induction,  291.  Illustrations,  292.  Func- 
tion of  the  imagination  in  hypothesis,  299.  Analysis  and 
synthesis,  300.  Requirements  of  a logical  hypothesis,  301. 
Consilience  of  inductions,  309.  Experimentum  Crucis , 310. 

Mill  and  Whewell  controversy,  312. 


CHAPTER  XHI 

Analogy 314 

Analogy  and  induction,  314.  Natural  kinds,  314.  Anal- 
ogy and  classification,  315.  Teleological  analogy,  317. 
Suggestion  the  chief  function  of  analogy,  323.  Require- 
ments of  true  analogy,  325.  Analogy  and  probability,  329. 

CHAPTER  XIV 

Probability  . 330 

Probability  and  causal  determination,  330.  Relation  to 
enumerative  induction,  332.  Various  kinds  of  inference  in 
sphere  of  probability,  333.  Coincidence  and  cause,  345. 
Circumstantial  evidence,  346.  Probability  and  method  of 
residues,  350. 


XVI 


CONTENTS 


CHAPTER  XV 

PAGE 

Empirical  Laws 351 

Various  degrees  of  probability  in  inference,  351.  Various 
kinds  of  empirical  laws,  352.  Empirical  uniformity  result- 
ing from  the  method  of  agreement,  357.  Empirical  laws 
and  laws  of  an  ultimate  nature,  357. 

CHAPTER  XVI 

Inductive  Fallacies 359 

Errors  of  perception,  360.  Errors  of  judgment,  362. 
Errors  of  imagination,  366.  Errors  of  the  conceptual  pro- 
cesses, 369.  The  psychological  nature  of  these  fallacies,  372. 

CHAPTER  XVII 

The  Inductive  Methods  as  applied  to  the  Various 

Sciences 374 

Method  varies  with  different  kinds  of  phenomena,  374. 
Difficulties  in  method  due  to  complexity  of  phenomena,  378. 
Phenomena  of  one  science  interpreted  in  the  light  of  others, 

380.  Deductive  method  of  some  sciences  replaced  by  the 
inductive,  381. 

CHAPTER  XVIII 

Historical  Sketch  of  Induction 385 

Socrates,  385.  Plato,  385.  Aristotle,  386.  Roger  Bacon, 

387.  Leonardo  da  Vinci,  388.  Telesius,  389.  Carnpa- 
nella,  389.  The  experimental  investigators,  390.  Francis 
Bacon,  390.  Locke,  392.  Newton,  393.  Herschel,  394. 


Whewell,  395.  Mill,  396. 

Logical  Exercises 399 

Index  435 


PART  I 


DEDUCTIVE  LOGIC 


CHAPTER  I 


THE  NATURE  OF  THOUGHT 

Logic  is  a word  derived  from  the  Greek  Aoyos,  which 
means  thought  or  reason ; and  in  this  origin  may  be  found 
the  essential  significance  of  logic, — that  it  treats  of  the 
nature  and  of  the  laws  of  thought.  Before  it  is  possible 
to  appreciate  the  characteristic  features  of  the  laws  of 
thought,  it  is  necessary  to  understand  the  general  nature 
of  the  processes  of  thought  themselves.  While  the  process 
of  thought  is  various,  its  most  common  and  conspicuous 
manifestation  may  be  described  as  that  phase  of  the  mind’s 
activity  which  regards  any  specific  object  which  may  be 
presented  to  it  in  the  light  of  the  general  body  of  knowl- 
edge. For  example,  a person  may  chance  to  pick  up  a stone, 
which  he  holds  in  his  hand  for  a moment  and  immediately 
throws  away.  It  has  been  in  the  focus  of  his  attention  for 
a fleeting  moment  only,  and  has  excited  no  activity  of 
thought  whatsoever.  He  has  observed  but  has  not  thought 
about  it.  Suppose,  however,  it  does  arrest  his  attention  and 
he  begins  to  think  about  it,  what  is  the  nature  of  this 
thinking  which  goes  on  in  his  mind  ? If  his  knowledge  of 
geology  is  meagre,  the  result  of  the  application  of  it  to  the 
special  object  of  inquiry  may  be  merely  the  assertion  that 
the  stone  which  he  holds  in  his  hand  is  some  kind  of  a 
fossil.  If,  however,  his  knowledge  is  more  extensive  and 
has  grown  out  of  a wide  experience,  he  will  be  able  no 
doubt  to  refer  the  fossil  in  question  to  its  proper  geological 
age,  and  to  give  some  satisfactory  description  of  the  general 
nature  and  habits  of  that  species  of  animals  to  which  it 

3 


4 


DEDUCTIVE  LOGIC 


belongs,  thus,  in  a measure  more  or  less  explicit,  recon- 
structing its  probable  life  history.  Thinking,  therefore, 
may  be  defined  in  one  of  its  aspects  at  least  as  the  process 
of  interpreting  the  special  by  the  general,  or  the  new  expe- 
rience by  the  old. 

This  definition  of  thought  may  be  further  illustrated  by 
the  word  reflection,  which  is  often  used  as  synonymous 
with  thought.  Thus  we  say  that  we  will  reflect  about  a cer- 
tain proposition,  which  is  equivalent  to  saying  we  will  think 
about  it.  The  process  of  reflection  is  essentially  one  of 
illumination.  The  very  word  reflection  suggests  the  light 
ray  which  flashes  from  one  object  of  vision  to  another;  so, 
also,  in  a figurative  sense,  it  signifies  the  illumination  which 
one  object  of  knowledge  sheds  upon  another.  In  the  reflect- 
ing mind,  the  new  element  of  experience,  whatever  it  may 
be,  is  held  in  the  focus  of  the  light  rays  which  converge  to 
that  point  from  all  the  surrounding  parts  of  the  general  body 
of  knowledge  until  its  essential  nature  is  fully  revealed. 

In  this  process  which  we  call  thinking,  or  reflecting,  there 
are  in  all  four  functions  involved. 

1.  The  first  function  of  thought  consists  in  the  trans- 
formation of  the  crude  data  of  knowledge  furnished  by 
the  senses  into  forms  of  such  a nature  that  they  can  be 
readily  used  in  the  various  operations  of  our  thinking 
processes.  The  form  which  thought  necessarily  assumes 
for  the  prosecution  of  its  own  activity  is  always  that  of 
a universal  idea;  that  is,  an  idea  which  possesses  a one- 
ness of  meaning  but  admits  of  an  indefinite  variety  of 
application.  The  universal  is  sometimes  called  a group 
idea,  or  a class  idea,  by  which  a number  of  individuals  are 
embraced  under  some  one  general  designation.  If  our  body 
of  knowledge  consisted  merely  in  the  total  number  of  par- 
ticular experiences  arranged  in  the  form  of  a series  wherein 
each  separate  term  remained  distinct  and  completely  uncon- 
nected with  any  other  term,  then  obviously  new  experiences 
could  be  added  to,  but  never  could  be  assimilated  with, 


THE  NATURE  OF  THOUGHT 


5 


such  a body  of  knowledge.  Indeed,  a disconnected  array  of 
isolated  experiences  would  hardly  merit  the  name  of  knowl- 
edge at  all.  On  the  contrary,  the  elements  constituting  the 
body  of  our  knowledge  must  be  so  related  and  coordinated 
that  similar  elements  fall  together  in  such  a manner  that 
a single  thought  form  shall  be  able  to  express  them  all. 
Thus,  when  a geologist  says  that  a certain  stone  is  a fossil, 
he  means  that  in  his  general  body  of  knowledge  he  has 
framed  an  idea  known  by  the  word  symbol  “ fossil,”  which 
embraces  under  it  innumerable  special  cases,  and  that  one 
of  these  is  the  stone  in  question.  Thus  objects  of  per- 
ception can  be  grasped  by  the  mind  and  become  definite 
objects  of  thought.  This  grasp  of  the  mind  by  which  a 
number  of  special  cases  are  held  together  by  a single  idea 
of  a nature  so  universal  as  to  comprehend  them  all  is  known 
as  the  process  of  conception,  and  the  universal  idea  itself 
which  is  the  result  of  that  process  is  known  as  the  concept. 
This  word  is  from  the  Latin  concapio,  to  take  together.  The 
corresponding  German  word  is  Begriff,  which  has  the  same 
root  as  our  English  word  “ grip.”  In  the  concept  the  mind 
grasps  all  the  essential  features  which  characterize  a given 
group  or  class  of  objects,  and  holds  them  together  in  such  a 
manner  as  to  constitute  an  elemental  thought  form.  The 
process  of  thinking,  therefore,  is  fundamentally  a conceptual 
process,  and  this  primary  function  of  thought  consists  in 
constructing  whatever  is  given  through  the  processes  of 
perception  into  the  forms  of  concepts. 

2.  The  second  function  of  thought  consists  in  the  reduc- 
tion of  the  total  mass  of  concepts  to  some  kind  of  systematic 
order.  Every  concept  as  it  is  formed  must  be  received  into 
the  general  body  of  knowledge  and  assigned  to  its  proper 
place  and  position.  The  concepts  must  be  arranged  in  their 
due  rank  and  order  according  to  their  natural  relations  of 
coordination  or  subordination.  In  order  that  our  concepts 
may  be  used  as  instruments  of  knowledge,  they  must  admit 
of  a constant  and  consistent  reference  to  the  general  system 


6 


DEDUCTIVE  LOGIC 


of  which  they  form  constituent  parts.  These  elemental 
forms  of  thought  must  have  their  origin  in  order  and  not  in 
chaos.  They  must  be  subject  to  underlying  laws  of  relation, 
and  not  to  accident  or  caprice.  Thus  the  botanist  not  only 
possesses  an  idea  of  the  general  nature  of  a certain  species 
of  plant,  that  is,  a concept  of  it,  but  he  knows  also  definitely 
its  particular  relation  to  the  classified  system  of  plants  as 
a whole.  He  is  able  therefore  to  describe  the  species  in 
question  by  the  relative  position  which  it  occupies  in  the 
system  itself.  Knowledge  of  the  species  is  obtained  not 
merely  through  an  understanding  of  what  it  is,  but  also  of 
what  its  proper  setting  may  be. 

3.  The  third  function  of  thought  consists  in  referring 
whatever  may  be  before  the  consciousness  as  the  object  of 
thought  to  its  appropriate  concept.  Such  a reference  is  a 
process  of  interpretation,  and  represents  the  central  and 
most  essential  feature  of  all  thinking.  This  mode  of  inter- 
pretation may  be  brought  about  in  several  ways. 

(a)  In  the  first  place,  any  one  portion  of  our  general 
body  of  knowledge  may  be  interpreted  in  the  light  of  some 
other.  Thus  by  way  of  interpretation  or  explanation  I may 
refer  one  concept  to  another  concept  which  embraces  it  as 
a smaller  class  or  group  within  a larger  one ; e.g.  the  Trap- 
pists  are  a Roman  Catholic  brotherhood. 

( b ) Again,  the  concept  lends  itself  to  a further  use  as  an 
instrument  of  knowledge,  by  revealing  the  various  charac- 
teristics which  constitute  its  nature  according  as  the  trend 
of  thought  at  the  moment  may  happen  to  emphasize  one  or 
another  of  them.  In  the  ordinary  processes  of  thought  we 
never  use  a concept  in  the  totality  of  its  significance.  We 
attend  only  to  a single  phase  of  the  concept’s  meaning  at  a 
time;  and  our  thought  selects  always  that  particular  phase 
of  the  meaning  which  is  pertinent  to  the  special  object  of 
thought  under  consideration.  Thus  the  concept,  govern- 
ment, is  an  exceedingly  complex  idea,  and  may  be  consid- 
ered from  various  points  of  view,  — as  to  its  general  nature, 


THE  NATURE  OF  THOUGHT 


7 


whether  democratic,  monarchial,  despotic,  etc. ; or  as  to  its 
special  functions,  whether  that  of  the  judicial,  legislative,  or 
executive.  The  concept  as  a complex  idea  may  always  be 
subjected  to  a more  precise  determination  by  the  concentra- 
tion of  thought  upon  one  or  more  of  its  special  attributes  or 
relations. 

(c)  In  the  third  place,  a particular  experience  in  the 
field  of  sense  perception  may  be  interpreted  by  referring  it 
to  the  appropriate  concept  of  which  it  may  be  regarded  as  a 
special  case.  The  knowledge  given  through  the  senses  is 
rendered  more  definite  by  this  reference  of  it  to  a concept 
which  serves  to  illumine  it. 

This  process  of  thought  which  renders  the  elements  of 
consciousness  more  definite  by  a reference  in  any  one  of  the 
three  ways  mentioned  above  to  some  interpreting  concept 
is  known  as  the  judgment.  There  is  a universal  tendency 
of  thought  to  transform  every  concept  into  the  form  of  a 
judgment,  because  the  very  presence  of  a concept  in  con- 
sciousness challenges  our  thought  to  express  some  definite 
assertion  concerning  it,  and  such  an  assertion  is  itself  a 
judgment.  As  long  as  there  is  sustained  interest  in  any 
concept  which  occupies  the  focus  of  attention,  there  is  a 
constant  play  of  thought  about  it ; we  turn  it  over  in  our 
minds ; we  examine  it  on  all  sides ; we  put  questions  to 
ourselves  about  it;  and  the  result  is  a series  of  judgments 
as  regards  its  nature  and  the  several  relations  which  it  sus- 
tains to  cognate  concepts.  Thus  our  general  knowledge 
serves  to  illumine  the  specific  portion  of  it  which  is  the 
special  object  under  contemplation.  So  also  when  the 
object  of  consciousness  is  a particular  object  of  sense  per- 
ception, we  form  a judgment  by  referring  it  to  its  appropri- 
ate concept.  Thus  in  the  judgment,  Arsenic  is  a poison,  we 
have  as  it  were  a cross-section  of  our  knowledge  in  general ; 
but  in  the  judgment,  this  substance  which  is  in  the  test- 
tube  before  me  contains  arsenic,  the  reference  is  to  a special 
object  in  the  field  of  vision  which  is  interpreted  by  means 
of  its  appropriate  concept. 


8 


DEDUCTIVE  LOGIC 


Every  new  experience  which  is  more  than  a fleeting  im- 
pression, and  which  is  drawn  into  the  field  of  our  attention, 
gives  rise  to  one  or  more  judgments  of  this  latter  kind.  As 
I am  writing,  I look  out  from  a hillside  which  commands  a 
wide  prospect;  and  as  I observe  the  various  objects  in  the 
field  of  vision,  my  thought  immediately  refers  them  to  their 
appropriate  concepts  by  way  of  more  definite  characteriza- 
tion. There  is  the  winding  road  through  the  valley,  sepa- 
rating the  green  meadow  from  the  wood  beyond;  in  the 
meadow  cows  are  grazing;  by  the  side  of  the  road  flows  a 
stream,  rushing  over  its  rocky  bed  and  losing  itself  in  the 
dark  shadows  of  the  wood ; in  the  distance  are  the  uplands 
again  bounded  by  the  horizon  line,  above  which  the  clouds 
are  hanging  low  and  threatening.  Such  a description  of  the 
various  objects  of  perception  within  a field  of  vision  forms  a 
series  of  particular  instances  referred  to  their  corresponding 
concepts.  They  are  simple  judgments  of  identification, — 
a reference  of  an  object  immediately  before  us  to  a familiar 
idea  which  through  its  word  symbols  satisfactorily  describes 
it.  Such  a scene  however  naturally  gives  rise  to  more  com- 
plex ideas,  which  represent  the  fourth  function  of  thought. 

4.  This  fourth  function  of  thought  consists  in  the  process 
of  unfolding  whatever  may  be  necessarily  implied  in  our 
judgments,  but  is  not  explicitly  asserted.  Thus  in  the  scene 
described  above,  I am  able  to  make  certain  statements  which 
are  warranted  by  the  facts,  but  which  are  not  the  result  of 
simple  observation.  I am  led  to  venture  the  assertion  that 
there  are  trout  in  the  stream  before  me ; that  by  reasonable 
skill  and  perseverance  a fisherman  may  hope  to  fill  his  creel 
there  in  a few  hours ; that  the  threatening  clouds,  the  east 
wind,  and  sultry  atmosphere  will  bring  rain;  and  that  it 
would  be  wise  under  such  conditions  to  fish  worm  rather 
than  fly.  Judgments  such  as  these  are  far  more  complex 
than  the  simple  judgments  of  identification  or  recognition. 
We  may  call  them  judgments  of  elaboration.  What  is  actu- 
ally given  is  combined  with  our  general  knowledge  in  such 


THE  NATURE  OF  THOUGHT 


9 


a manner  as  to  render  explicit  the  full  measure  of  all  which 
is  necessarily  implied.  Thus  the  assertion  that  the  stream 
contains  trout  is  based  upon  an  experience  of  many  years, 
and  in  this  way  the  past  is  used  as  a meaus  of  interpreting 
the  present.  In  like  manner  my  past  experience  of  atmos- 
pheric conditions  enables  me  to  interpret  the  present  condi- 
tions as  indicating  the  approach  of  rain.  Moreover,  the 
dark  and  stormy  day  is  judged  to  be  more  suitable  for  worm 
than  fly  fishing,  because  on  account  of  the  coming  rain  the 
natural  flies  will  not  be  on  the  wing,  and  the  rain  itself  will 
wash  from  the  hillsides  and  banks  into  the  stream  grubs 
and  worms,  which  the  expectant  trout  will  be  in  readiness 
to  take.  My  general  knowledge  has  enabled  me  in  this 
particular  case  to  make  statements  which  go  beyond  that 
which  is  actually  perceived,  but  which  nevertheless  I am 
constrained  to  believe  true,  because  necessitated  by  what  is 
known.  And  this  is  the  essential  feature  of  all  inference. 

But  inference  is  not  confined  to  the  interpretation  of  that 
which  is  given  in  perception.  It  may  serve  also  to  interpret 
any  part  of  our  general  body  of  knowledge  by  any  other 
part,  or  by  the  whole.  Thus  two  judgments  of  a universal 
nature  may  be  brought  together  in  such  a manner  that  their 
combination  furnishes  elements  of  knowledge  which  are  not 
given  by  either  judgment  separately.  We  know,  for  in- 
stance, that  the  sum  of  the  angles  formed  on  the  same  side 
of  a straight  line  at  a given  point  equals  two  right  angles; 
also,  that  the  exterior  angle  formed  by  extending  a side  of  a 
triangle  equals  the  two  opposite  and  interior  angles.  These 
two  judgments,  when  put  together,  necessitate  the  infer- 
ence that  the  sum  of  the  angles  of  a triangle  equals  two 
right  angles.  Inference  therefore  is  essentially  a process 
by  which  our  thought  combines  given  elements  of  knowledge 
in  such  a way  that  the  result  contains  something  which  the 
given  elements  in  their  isolation  fail  to  disclose. 

There  are  some  general  considerations  in  reference  to  these 
four  functions  of  thought  which  should  be  presented.  In  the 


10 


DEDUCTIVE  LOGIC 


first  place,  the  word  function  itself  is  significant.  It  in- 
dicates an  activity  which  is  dependent  upon  other  activities 
correlated  with  it.  Each  of  the  four  functions  of  thought  is 
closely  connected  and  coordinated  with  the  other  functions, 
and  no  one  is  complete  in  itself.  The  concept  is  an  essential 
element  of  the  judgment,  for  the  judgment  is  merely  the 
concept  rendered  definite  through  assertion.  Moreover,  in- 
ference is  a process  which  consists  essentially  in  the  expan- 
sion and  elaboration  of  our  judgments.  Inference  is  itself  a 
judgment,  only  it  is  a judgment  which  is  reached  indirectly. 
And  in  the  formation  of  any  judgment  it  is  exceedingly 
difficult  to  eliminate  altogether  the  inferential  elements, 
inasmuch  as  every  judgment  contains  more  than  is  actually 
given  in  perception,  or  in  a series  of  perceptions.  The  result 
rests  largely  upon  that  which  is  necessitated  by  our  general 
knowledge,  and  this  is  essentially  inference. 

In  these  coordinated  relations  which  unite  concept,  judg- 
ment, and  inference,  it  is  natural  to  regard  judgment  as  the 
central  function  of  thought.  From  this  point  of  view  the 
concept  may  then  be  defined  as  the  judgment  in  its  potential 
form ; that  is,  the  concept  contains  in  an  indefinite  way  all 
the  possible  elements  of  knowledge  which  it  is  the  function 
of  the  judgment  to  make  explicit.  The  inference  is  the 
judgment,  as  we  have  seen,  exhibited  in  its  relation  to  other 
judgments  upon  which  it  depends  as  the  warrant  of  its 
validity.  The  concept  is  an  abridged  form  of  judgment, 
while  the  inference  is  an  expanded  form ; and  the  unit  of 
thought,  therefore,  which  lies  at  the  basis  of  all  thought 
processes  is  the  judgment.  It  is  to  thought  what  the 
element  is  to  chemistry. 

Again  it  is  to  be  observed  that  in  the  process  of  inter- 
preting a given  object  of  knowledge  by  means  of  its  corre- 
sponding thought  form,  it  happens  that  the  object  in  question, 
say  a given  object  in  the  field  of  vision,  will  in  some  measure 
at  least  modify  the  thought  form  to  which  it  is  referred. 
Thus  every  new  experience  is  both  interpreted  by  our 


THE  NATURE  OE  THOUGHT 


11 


general  body  of  knowledge,  and  also  in  turn  widens  the  range 
of  that  knowledge  and  changes  its  nature  to  a greater  or 
less  extent.  Especially  is  this  true  concerning  any  object 
of  knowledge  which  is  so  new  as  to  be  wholly  unfamiliar. 
There  is  then  no  appropriate  thought  form  to  which  we  can 
refer  it.  We  must  so  analyze  the  properties  of  the  object  in 
question  and  compare  it  with  other  instances  of  the  same  gen- 
eral kind,  as  to  construct  a basis  for  the  formation  of  a con- 
cept which  shall  embrace  the  new  order  of  phenomena  under 
consideration.  Such  a new  concept  has  to  be  fitted  into  the 
main  body  of  concepts,  and  the  process  of  readjustment 
among  the  old  concepts  is  sometimes  a most  complex  and 
difficult  one.  This  is  illustrated  in  a striking  manner  by 
the  newly  formed  concept  of  radium  and  the  various  prop- 
erties of  radio-activity.  To  receive  this  new  concept  into 
the  main  body  of  concepts  requires  a readjustment  of  our 
former  ideas  of  matter,  conservation  of  energy,  etc.,  which 
is  almost  revolutionary. 

Again,  among  the  philosophical  sciences,  logic  is  usually 
grouped  with  ethics  and  aesthetics  under  the  general  class 
of  the  so-called  normative  sciences.  A normative  science  is 
one  which  refers  all  its  phenomena  to  some  standard,  or 
norm  of  value  to  which  they  are  required  to  conform.  The 
standard  in  ethics  is  that  of  the  right  or  the  good;  in 
aesthetics,  of  beauty ; and  in  logic,  of  truth.  Truth  may 
be  defined  as  correspondence  with  reality.  The  real  is  the 
world  as  it  is  constructed  by  us  in  consciousness.  It  is 
coextensive  with  the  whole  received  body  of  knowledge. 
It  is  the  world  which  is  revealed  to  us  through  the  senses, 
it  is  true ; but  at  the  last  analysis  it  is  that  world  as  we 
interpret  and  understand  it. 

To  say  therefore  that  the  logical  demand  of  our  concepts 
is  that  they  must  be  true  signifies  that  every  concept  must 
clearly  and  adequately  embody  the  essential  features  of  all 
the  particular  instances  in  experience  which  have  formed 
the  basis  of  its  derivation ; the  concept  moreover  must  be 


12 


DEDUCTIVE  LOGIC 


capable  of  a constant  reference,  that  is,  it  must  not  contain 
any  element  of  variability  which  prejudices  its  integrity  as 
a concept.  To  say  that  a judgment  must  be  true  signifies 
that  when  the  judgment  expresses  the  general  relation  of 
any  concepts  to  each  other  within  the  same  system,  it  must 
conserve  the  general  order  which  characterizes  the  system 
as  a whole,  and  all  interrelated  parts  of  it ; and  when  the 
judgment  is  of  the  form  of  a particular  experience  referred 
to  its  appropriate  concept,  then  all  such  references  must  be 
exact.  To  say  that  an  inference  must  be  true  signifies  that 
the  conclusion  reached  through  the  process  of  inference 
must  be  of  such  a nature  that  every  element  of  it  will  find 
complete  warrant  in  that  which  is  adduced  as  its  ground. 
The  logical  standard,  therefore,  which  must  be  realized  in 
all  cases  demands  clear  and  adequate  concepts  of  a constant 
meaning  arranged  in  an  orderly  system,  so  that  every 
reference  to  it  of  any  particular  object  of  thought  must  be 
exact,  and  every  inference  based  upon  it  must  be  valid. 
While  truth  may  manifest  itself  in  many  ways  as  clearness, 
adequacy,  constancy,  consistency,  exactness,  or  validity, 
nevertheless  these  are  all  but  various  instances  of  a single 
elemental  principle  which  underlies  the  ultimate  standard 
of  logical  thinking. 


CHAPTER  II 


THE  CONCEPT 

The  concept  as  a form  of  thought  embraces  a number 
of  phenomena  which,  however  much  they  may  differ,  have 
nevertheless  an  underlying  unity.  The  ratio  of  the  elements 
of  similarity  to  those  of  diversity  in  our  concepts  is  by  no 
means  a constant  one,  but  admits  of  considerable  variation. 

1.  In  the  first  place,  the  diversity  may  be  reduced  sub- 
stantially to  zero,  as  for  instance  in  such  a concept  as  that 
of  a silver  dollar.  The  differences  which  exist  between  the 
several  particular  cases  of  this  general  concept  are  so  minute 
as  to  be  overlooked ; the  similarity  alone  attracts  the  at- 
tention. Each  one  is  an  exact  copy  of  every  other,  and  the 
idea  of  any  diversity  is  here  practically  eliminated. 

In  reality,  however,  no  two  phenomena  are  precisely 
alike.  As  Leibniz  once  remarked,  “No  two  leaves  on  the 
same  tree  are  alike.”  And  Plato  in  the  same  vein  has  said 
that  “ If  two  things  were  exactly  alike,  there  would  not  be 
two  but  one.”  Therefore,  while  the  element  of  diversity 
may  be  reduced  to  zero  as  regards  its  practical  relevancy 
and  as  regards  the  essential  significance  of  the  concept  in 
question,  nevertheless  it  is  always  present  in  some  appre- 
ciable degree  and  may  be  discovered  to  a discriminating 
observer. 

2.  There  is  a second  class  of  concepts  wherein  the  diver- 
sity is  more  apparent,  and  yet  the  likeness  is  quite  as 
obvious.  Thus  the  concept,  dog,  embodies  all  the  charac- 
teristic features  of  the  dog  race,  and  yet  is  so  elastic 
and  ample  an  idea  as  to  hold  in  one  and  the  same  mental 
grasp  such  diverse  breeds  as  the  mastiff,  the  bull-dog, 

13 


14 


DEDUCTIVE  LOGIC 


the  French  poodle,  the  greyhound  and  dachshund.  A con- 
cept such  as  this  is  typical  of  the  general  run  of  concepts 
which  require  no  unusual  penetration  to  disclose  the  funda- 
mental elements  of  similarity  in  spite  of  the  wide  range  of 
differences. 

3.  There  is,  however,  a third  class  of  concepts  which 
require  more  than  ordinary  insight,  it  may  be  the  insight  of 
genius,  in  order  to  discover  the  unity  which  lies  hidden  be- 
neath an  obscuring  mass  of  manifold  differences.  It  required 
the  analytic  mind  of  a Newton  to  grasp  under  one  concept 
such  diverse  phenomena  as  the  fall  of  a body  to  the  earth 
and  the  moon’s  revolution  about  its  orbit.  In  the  one  case 
there  is  motion  in  a straight  line,  in  the  other  the  motion 
is  in  the  path  of  an  ellipse ; in  the  one  the  body  actually 
falls  to  the  earth,  in  the  other  it  is  forever  falling  but  never 
falls.  Nevertheless,  the  two  are  similar.  The  course  of 
the  moon  may  be  resolved  into  two  distinct  motions ; the  one 
centripetal,  which  is  a direct  falling  toward  the  earth,  the 
other  the  centrifugal,  which  holds  the  former  in  check  and 
modifies  the  direct  fall  toward  the  earth  so  that  the  result 
is  the  present  elliptical  orbit  of  the  moon.  Therefore  it  may 
be  truly  said  that  the  moon  is  always  falling  toward  the 
earth  in  a manner  precisely  similar  to  that  of  the  ordinary 
falling  body  upon  the  earth’s  surface.  The  only  difference 
is  the  counter  force  which  is  operative  in  the  one  case  and 
not  in  the  other.  Such  a difference  however  so  obscures 
the  general  features  of  resemblance  in  the  resulting  phe- 
nomena that  a surface  observation  devoid  of  any  deeper 
reflection  may  pronounce  them  so  different  as  to  possess  no 
point  in  common.  It  is  characteristic  of  the  trained  mind 
that  it  is  able  to  penetrate  beneath  the  surface  and  discover 
points  of  similarity  which  escape  the  notice  of  unreflecting 
observation.  Fortunately  for  the  generality  of  intelligence, 
the  phenomena  of  human  experience  for  the  most  part  fall 
together  into  natural  groups  whose  underlying  bond  of  unity 
is  perfectly  obvious.  Nature  is  so  prodigal  of  her  creations 


THE  CONCEPT 


15 


that  innumerable  individuals  of  the  same  species  are  forced 
upon  our  attention.  The  common  events  of  life  repeat  them- 
selves with  a regularity  which  compels  the  recognition  of  a 
constant  and  common  principle  as  their  basis.  Therefore  it 
becomes  a natural  habit  of  mind  to  see  things  together  by 
reason  of  their  common  features.  The  most  primitive  of  all 
our  judgments,  and  that  which  lies  at  the  foundation  of  all 
other  judgments,  is  that  which  is  based  upon  the  recognition 
of  similarity  among  phenomena.  The  concept  has  its  ori- 
gin in  the  recognition  of  similarity  among  several  percepts.1 
As  Schopenhauer  has  remarked,  “We  get  the  stuff  and 
content  of  our  concepts  from  observation.”  In  our  obser- 
vation, the  various  instances  of  some  one  general  kind  of 
phenomena  fall  together  in  our  minds  on  account  of  their 
similarity.  They  form  a series  of  similar  percepts,  each 
term  of  which  differs  from  every  other  term,  and  yet  all  in 
a certain  sense  are  alike.  The  mind  grasps  the  essential 
features  of  similarity,  fusing  them  together  according  to  an 
underlying  unity  which  persists  in  spite  of  the  differences. 
The  result  is  the  concept.  In  such  a process,  the  mind  has 
subjected  the  various  percepts  to  an  analysis  which  sepa- 
rates whatever  is  peculiarly  individual  in  each  instance 
from  the  elements  which  are  characteristic  of  the  series  as 
a whole.  This  is  essentially  a process  of  abstraction ; it  is 
what  Aristotle  calls  a^mpevi s.  There  is  also  a complement- 
ary process  of  synthesis,  v-poo-Oeais  according  to  Aristotle, 
which  consists  in  building  up  the  common  elements  obtained 
by  the  analysis  into  a complete  whole.  The  resulting 
product  is  in  no  sense  merely  an  image  in  the  mind  of  the 
blended  percepts,  but  is  essentially  an  ideal  construction  of 
thought  which  is  sufficiently  comprehensive  and  elastic  to 
admit  of  application  to  all  particular  cases  of  it.  These 
processes  of  separating  and  uniting,  of  tearing  down  and 
building  up,  of  analysis  and  synthesis,  have  become  so  con- 

1In  the  terminology  of  psychology,  the  process  of  perceiving  is  called 
perception  ; the  resulting  product,  however,  is  known  as  the  percept. 


16 


DEDUCTIVE  LOGIC 


firmed  a mental  habit  that  we  are  not  conscious  of  them,  but 
come  to  regard  our  concepts  in  the  light  of  original  mental 
possessions  rather  than  thought  forms  which  we  ourselves 
have  fashioned  out  of  the  various  phenomena  in  experience. 

The  unconscious  blending  together  of  the  essential  charac- 
teristics of  a group  of  phenomena  forms  a concept  which  is 
at  first  barely  more  than  a general  impression,  a vague 
mental  grasp  of  the  kind  of  objects  represented  by  it.  The 
mind  has  not  yet  worked  over  its  first  impressions  and  has 
not  formed  the  crude  data  of  its  perception  into  clear  and 
adequate  concepts.  The  concept  at  this  preliminary  stage 
of  its  evolution  is  called  empirical,  signifying  that  it  is  the 
result  of  a superficial  experience  which  has  been  subjected 
to  no  critical  analysis  whatsoever.  The  word  empirical  in 
philosophy  signifies  whatever  is  the  result  of  experience;  it 
has,  however,  a secondary  meaning  which  implies  that  the 
experience  in  question  is  a limited  one.  It  is  in  this  sec- 
ondary sense  that  the  phrase  empirical  concept  is  used. 
On  the  other  hand,  the  logical  or  scientific  concept,  as  it 
is  often  called,  is  one  which  has  been  formed  as  the  result 
of  some  conscious  effort  to  analyze  the  various  phenomena 
which  form  the  basis  of  the  concept  in  question  so  as  to 
obtain  a clear  and  adequate  idea  of  their  essential  charac- 
teristics. The  logical  concept  differs  from  the  empirical  in 
the  following  particulars : — 

1.  The  logical  concept  is  always  characterized  by  a grow- 
ing loss  of  particularity.  The  preliminary  rough  draft  of 
our  concepts  always  shows  the  coloring  of  the  particular 
instances  whence  they  have  arisen.  Our  first  experiences 
are  necessarily  few  in  number,  and  they  are  not  sufficiently 
numerous  to  afford  a basis  for  the  elimination  of  all  charac- 
teristics which  are  not  essential.  Certain  features  which 
may  be  common  to  a limited  number  of  instances  will  often 
disappear  when  that  number  is  increased.  The  disappear- 
ance of  such  characteristics  or  their  appearance  in  a sporadic 
manner  merely  proves  that  they  do  not  belong  to  the  essence 


THE  CONCEPT 


17 


of  the  concept.  It  is  an  evidence  of  an  ignorant  or  untrained 
mind  that  it  associates  its  concepts  with  particular  experi- 
ences. Such  an  intellect  we  are  pleased  to  call  provincial 
or  insular.  The  nature  of  the  logical  concept  is  always 
indicated  by  its  independence  of  the  special  case.  Thus 
the  concept  of  gravitation  is  not  confined  to  the  earth’s 
attraction  of  bodies  upon  its  surface.  It  rises  above  such 
a particular  instance,  and  presents  the  idea  of  universal 
attraction,  of  which  the  force  of  gravitation  upon  the  earth 
is  but  a small  and  insignificant  instance. 

The  objection  has  been  urged  by  Berkeley  for  instance 
that  this  growing  loss  of  particularity  in  the  concept  in- 
dicates an  increasing  indefiniteness,  inasmuch  as  the  elimina- 
tion of  one  particular  attribute  after  another  tends  to  reduce 
the  concept  itself  to  a bare  form  stript  of  all  definite  features. 
Consequently,  it  is  insisted,  our  concept  of  a rose  must  be  one 
devoid  of  any  specific  color,  form,  or  fragrance,  and  our  con- 
cept of  a dog  must  be  one  of  no  particular  breed,  habit,  or 
disposition ; concepts,  therefore,  are  but  the  spectral  forms 
of  real  objects.  This  view,  however,  is  based  upon  a radical 
misunderstanding  of  the  essential  nature  of  a concept.  For 
the  concept  is  freed  from  the  particular  attributes  which 
characterize  the  various  percepts  only  in  a certain  sense. 
While  these  attributes  are  not  preserved  as  such  in  the 
concept,  they  are  nevertheless  conserved.  The  particular 
attribute  of  color,  or  of  form,  or  of  habit  is  indeed  dropped 
out  of  mind  in  framing  the  concept,  but  there  is  always  a 
compensation  for  the  loss  of  the  particular  by  substituting 
in  its  place  the  possibility,  not  only  of  the  attribute  in 
question,  but  of  all  others  of  the  same  general  kind.  Instead 
of  the  particular  we  have  the  potential  which  admits  of  an 
indefinite  degree  of  variation.  Thus  the  concept  of  a rose 
admits  of  any  shade  of  color  whatsoever  which  is  compatible 
with  the  whole  range  of  experience  regarding  roses.  In 
this  adaptability  to  all  possible  varieties  of  color,  the  poten- 
tial color  of  the  concept  is  vastly  richer  in  content,  and  far 


18 


DEDUCTIVE  LOGIC 


more  comprehensive,  than  the  single  color  of  any  particular 
rose  could  possibly  be.  So,  also,  the  concept  of  a dog  is 
not  confined  to  a particular  breed;  it  embraces  the  potential 
of  all  the  possible  breeds  of  dogs.  Indeed,  the  mental 
process  of  constructing  a concept  may  be  regarded  as  that 
of  transforming  the  various  observed  attributes  of  the  same 
general  order  into  a potential  attribute  which  is  lodged  in 
our  minds  as  a comprehensive  symbol  embracing  every 
possible  variety  of  detail. 

This  potential  variation  in  any  concept  should  not  remain 
indefinite  and  vague,  but  should  have  definitely  prescribed 
limits.  Thus  the  color  possibility  of  the  concept  of  a rose 
possesses  a very  wide  range  of  variation ; that  of  the  violet, 
however,  is  narrowly  circumscribed.  The  leaf  of  a beech 
tree  shows  a definite  pattern,  which  is  preserved  in  the 
midst  of  a variation  which  is  essentially  one  of  size  alone, 
and  that  within  known  and  easily  recognized  limits.  In  the 
leaf  of  the  sassafras  tree  there  is  a far  wider  possibility  of 
variation.  On  one  and  the  same  tree  of  this  species  there  are 
leaves  of  three  distinct  patterns.  Whatever  may  be  our  con- 
cept of  the  sassafras  leaf,  it  must  certainly  provide  for  this 
characteristic  variation  of  form.  Moreover,  the  range  of 
variation  may  itself  be  subject  to  a variation  under  chang- 
ing circumstances.  The  leaf  of  the  maple  is  in  its  normal 
appearance  green.  It  admits  of  a wide  variation  of  shade  but 
always  within  the  limits  of  the  one  color.  In  the  autumn 
tints,  however,  there  is  a remarkable  expansion  of  the  range 
of  variation,  the  green  turning  into  the  various  shades  of 
brown,  yellow,  red,  gold,  and  crimson.  The  possibility  of  a 
wide  range  of  variation  in  the  attributes  of  our  concepts 
render  them  as  thought  forms  exceedingly  elastic  in  the 
processes  of  thinking,  while,  on  the  other  hand,  the  definite 
limitation  of  their  possible  variation  renders  them  quite  as 
serviceable  for  exact  reference  and  determination.  There  is 
thus  a double  gain  both  of  precision  and  facility  in  the 
exercise  of  our  thought  activity. 


THE  CONCEPT 


19 


2.  There  is  a second  characteristic  of  the  logical  concept 
in  distinction  from  the  roughly  generalized  empirical  con- 
cept ; namely,  that  it  is  freed  from  all  dependence  upon  any 
mental  picture  in  order  to  render  it  clear  and  intelligible. 
This  feature  of  the  logical  concept  grows  out  of  the  former 
given  above,  — the  growing  loss  of  particularity;  for  the 
particular  can  be  represented  to  thought  in  the  form  of  a 
memory  image  of  the  original  experience.  Not  so,  however, 
with  the  universal  idea  which  lies  at  the  basis  of  the  concept. 
The  concept  is  not  a composite  picture  in  the  mind  of  a 
series  of  percepts.  As  far  as  a mental  picture  might  sug- 
gest resemblances,  we  would  naturally  classify  together  the 
whale  and  the  fish,  or  the  bat  and  the  bird.  Dissociated 
however  from  the  representations  of  the  outer  appearance 
of  these  animals,  the  bat,  as  regards  the  essential  elements 
which  go  to  make  up  the  concept,  is  far  more  closely  allied 
to  the  whale  than  to  the  bird.  The  mental  picture  is  in- 
deed a help  to  our  thinking,  but  strong  minds  must  learn  to 
forego  such  adventitious  aid.  The  undeveloped  mind  — that 
of  the  savage,  or  the  child  — is  dependent  upon  pictures, 
symbols,  or  figurative  representations.  In  the  process  of 
education,  as  the  mental  activity  becomes  trained  and  dis- 
ciplined, the  need  of  colored  chalk,  of  illustrative  diagrams, 
and  of  picture-books,  becomes  less  and  less  in  evidence. 
In  the  evolution  of  the  religious  sentiment,  this  is  notice- 
able in  a marked  degree.  The  early  religions,  notably  that 
of  Judaism,  endeavored  to  convey  spiritual  truth  through 
an  appeal  to  the  senses  mediated  by  a brilliant  symbolism. 
This,  however,  was  superceded  by  that  religion  which  laid 
stress  upon  a worship  in  spirit  and  in  truth,  with  no  in- 
direct appeal  to  the  thought  through  the  senses,  but  by 
means  of  ideas  which  directly  enlightened  the  eyes  of  the 
understanding.  An  appreciation  of  the  truth  in  this  wise  is 
essentially  logical  inasmuch  as  the  truth  appears  in  a form 
which  appeals  immediately  to  the  reason. 

3.  A third  characteristic  of  the  logical  concept  is  its 


20 


DEDUCTIVE  LOGIC 


tendency  to  progressive  differentiation ; that  is,  a breaking  up 
into  smaller  concepts  which  are  more  precisely  determined, 
and  more  distinctly  separated  in  thought  one  from  the 
other.  The  first  rough  concepts  which  are  formed  embrace 
without  discrimination  all  sorts  of  individual  instances  which 
may  happen  to  present  any  surface  resemblances  whatso- 
ever. The  child  may  have  at  first  but  one  vague  concept 
which  applies  equally  well  to  a cow,  a horse,  and  a mule. 
Later  in  the  growth  of  knowledge,  this  indefinite  concept 
breaks  up  into  more  definite  ones,  and  the  child  learns  to 
discriminate  between  the  cow  and  the  horse,  and  between 
the  horse  and  the  mule.  Wherever  there  is  knowledge 
which  is  comprehensive  and  exact,  the  corresponding  con- 
cepts are  nicely  differentiated  and  precisely  determined. 
For  most  persons,  it  is  a sufficient  identification  of  a bird 
to  recognize  it  as  a hawk.  But  for  the  ornithologist  such 
a reference  is  altogether  too  general  and  indefinite.  He 
wishes  to  know  which  one  of  the  several  different  species 
of  hawk  the  particular  bird  may  happen  to  be.  Nothing  is 
gained  however  by  the  mere  multiplication  of  the  number 
of  concepts,  unless  at  the  same  time  we  are  able  to  discrimi- 
nate between  them.  The  discriminating  mind  is  essentially 
the  logical  mind.  The  means  by  which  our  concepts  may 
receive  more  precise  determination  will  be  discussed  later 
in  the  chapter  on  the  negative  judgment. 

There  are  two  ways  by  which  our  concepts  may  be  broken 
up  so  as  to  give  rise  to  new  concepts.  The  one  has  already 
been  mentioned,  — the  analysis  of  the  concept  into  smaller 
and  smaller  groups,  each  group,  however  small,  represent- 
ing a complete  whole,  or  complex  of  attributes.  The  other 
does  not  regard  a complex  of  attributes  which  together 
constitute  the  characteristic  features  of  a distinct  species  of 
plant  or  animal ; it  regards  the  rather  some  single  attribute 
and  concentrates  the  attention  upon  that.  This  attribute  is 
first  viewed  in  all  the  particular  instances  where  it  occurs, 
and  then  fashioned  into  the  form  of  a concept  by  considering 


THE  CONCEPT 


21 


it,  in  and  by  itself,  quite  apart  from  any  of  tbe  instances 
which  illustrate  it.  Such  a concept  is  known  as  an  abstract 
concept.  It  is  our  idea  of  a particular  quality  or  attribute 
of  a thing  apart  from  the  thing  itself.  The  concrete  con- 
cept, on  the  other  hand,  is  our  idea  of  a thing  as  composed 
of  a complex  of  attributes,  and  none  of  them  separated  in 
thought  from  the  thing  in  which  they  all  inhere.  Thus  we 
have  the  abstract  concept  of  motion  as  distinct  from  the 
concrete  concept  of  a moving  body ; the  abstract  concept  of 
a sweet  or  sour  flavor  as  distinct  from  the  concrete  concept 
of  sugar,  or  of  a lemon,  in  which  the  attributes  sweet  and 
sour  may  find  expression.  So  also  we  have  the  abstract 
concepts  of  activities  apart  from  any  actors,  such  as  speak- 
ing, swimming,  fighting,  etc.  There  may  be  abstract  con- 
cepts not  merely  of  attributes  and  activities,  but  also  of 
relations  which  may  exist  between  different  objects  of  per- 
ception, or  between  concepts  as  the  case  may  be,  quite  apart 
from  the  objects  or  concepts  thus  related,  such  as  the  con- 
cept of  cause  and  effect,  of  organization,  of  sequence,  or  of 
coexistence.  There  may  be  also  abstract  concepts  involving 
a combination  of  several  attributes,  and  yet  held  apart  from 
any  definite  thing  or  object  of  knowledge  in  which  they 
inhere,  such  as  the  complex  concepts  of  freedom,  of  philan- 
thropy, of  the  good,  the  true,  the  beautiful.  The  possi- 
bility of  the  various  forms  of  abstract  concepts  and  of  the 
resulting  combinations  which  may  be  made  out  of  the  sepa- 
rated elements  is  indeed  without  limit.  Our  logical  faculty 
is  thus  given  an  indefinite  scope.  The  ability  to  combine 
the  given  elements  of  knowledge  into  new  forms  gives  to 
our  thought  a mighty  instrument  of  discovery  and  of 
progress. 

4.  There  is  still  another  characteristic  of  the  logical  in 
distinction  from  the  merely  empirical  concept,  a character- 
istic, however,  which  is  realized  only  in  that  higher  order 
of  concepts  which  merit  the  designation  of  scientific.  The 
nature  of  these  concepts  is  radically  distinct  from  that  of 


22 


DEDUCTIVE  LOGIC 


the  most  accurately  formulated  concepts  of  the  kind  which 
has  so  far  been  described.  Instead  of  representing  a corre- 
lated nexus  of  common  characteristics  which  discover  them- 
selves to  observation  in  the  several  special  cases,  this  new 
order  of  concepts  represent  rather  the  fundamental  con- 
structive principle,  which  both  underlies  the  actual  produc- 
tion of  every  particular  instance,  and  also  serves  to  preserve 
the  integrity  and  constancy  of  its  being  as  well.  Such  a prin- 
ciple may  assume  various  forms.  It  may  express  simply 
the  method  of  producing  the  different  instances  which  fall 
under  a single  concept.  Thus  the  concept  of  a conic  section 
represents  the  several  sections  which  may  be  made  of  a cone, 
according  as  the  angle  of  the  cutting  plane  is  varied.  There 
will  result  consequently  either  a point,  straight  line,  circle, 
ellipse,  parabola,  or  hyperbola.  A mere  observation  of  the 
general  features  of  these  lines  would  never  disclose  their 
common  nature.  They  fall  together  in  one  and  the  same 
group  on  account  of  their  common  origin,  while  a simple 
variation  in  the  manner  of  their  production  gives  rise  to  a 
pronounced  differentiation  in  the  results. 

Again  the  constructive  principle  may  represent  a summa- 
tion of  all  the  component  elements  of  the  object  in  ques- 
tion, with  possibly  the  formula  of  their  relative  proportions 
added.  Thus  the  concept  of  sulphuric  acid  can  be  repre- 
sented by  the  symbol,  H2S04,  an  exact  statement  of  the 
chemical  elements  in  the  proper  proportions  which  consti- 
tute the  essential  nature  of  the  compound.  A concept  of 
this  kind  is  very  different  from  that  concept  of  sulphuric 
acid  which  represents  its  several  properties  and  affinities. 

Again,  this  constructive  principle  may  appear  in  the 
form  of  a law  which  is  operative  in  producing  and  sustain- 
ing the  various  organisms  which  may  be  referred  to  it. 
Thus  the  concept  of  natural  selection  represents  a most 
comprehensive  law,  which  explains  the  origin  of  new 
species  in  the  evolution  of  natural  organisms.  Every 
species  has  its  own  constructive  principle,  which,  if  discov- 


THE  CONCEPT 


23 


ered,  would  form  the  truest  and  most  satisfactory  concept 
of  that  species.  These  various  forms  of  the  concept  repre- 
senting a constructive  principle  rather  than  a mere  complex 
of  common  attributes  are  known  by  the  one  name  of  gen- 
etic  concepts ; that  is,  concepts  which  refer  to  the  com- 
mon origin  of  a class  of  particular  instances,  rather  than 
to  the  characteristic  features  of  their  common  nature. 

There  now  remains  to  be  considered  a topic  of  consider- 
able interest  and  importance,  namely,  the  relation  of  the 
concept  to  the  word  which  serves  as  its  symbol.  As  a 
symbol  the  word  does  not  exist  for  itself,  but  only  for  the 
meaning  which  it  represents.  A symbol  always  refers  to 
something  which  lies  outside  of  itself,  and  language  is  a 
system  of  symbols  by  means  of  which  thought  finds  signifi- 
cant expression.  The  word  Aoyos  has  a twofold  meaning 
in  Greek  — (a)  the  thought  itself  and  ( b ) the  word  or  words 
which  stand  for  the  thought.  Aristotle  calls  the  one  6 tau 
or  6 iv  rrj  i//v\rj  Aoyos,  and  the  other  6 !£a>  Aoyos,  — that  is, 
the  one,  the  inner  logic ; the  other,  the  outer  logic.  Lan- 
guage, therefore,  is  the  external  symbol  of  the  inner  thought. 
We  have  seen  that  the  logical  concept  is  characterized  by 
a freedom  from  all  entanglements  with  any  particular  per- 
cepts, or  anything  like  a picture  representation  of  the 
same.  In  this  respect,  the  word  as  a symbol  forms  a most 
excellent  vehicle  for  the  expression  of  concepts  in  their 
pure  thought  significance.  For  the  word  is  perfectly  color- 
less and  is  freed  from  all  local  or  temporal  associations. 
The  growth  of  language  has  paralleled  in  this  respect  the 
growth  of  thought,  inasmuch  as  there  has  been  a constant 
tendency  for  words  to  lose  whatever  original  associations 
of  a particular  or  pictorial  nature  they  may  have  had.  The 
Hebrew  word  for  anger  was  derived  from  a root  which 
signified  the  boiling  over  of  a pot  of  water,  a suggestive 
picture  of  the  heat  and  energy  of  passion.  This  primitive 
picture,  however,  has  passed  away  and  only  the  significant 
thought  remains.  So,  also,  the  word  green  meant,  according 


24 


DEDUCTIVE  LOGIC 


to  its  derivation,  the  color  of  growing  things,  the  green 
natural  objects;  but  now  its  meaning  has  burst  these  limita- 
tions and  possesses  a far  wider  scope. 

There  is  also  a parallel  differentiation  of  words  accom- 
panying the  progressive  differentiation  of  thought.  Pro- 
fessor Max  Muller  refers  to  the  fact  that  the  Hawaiiaus 
have  only  one  word  to  express  the  various  ideas  of  love, 
friendship,  gratitude,  kindness,  and  respect.  To  discrimi- 
nate between  the  different  shades  of  meaning  which  these 
several  ideas  signify,  a corresponding  variety  of  verbal 
symbols  has  been  found  necessary.  Thus  the  inner  and  the 
outer  thought  have  progressed  together,  and  the  line  of  prog- 
ress is  always  toward  a more  complete  definiteness  of  mean- 
ing, in  which  the  finer  distinctions  of  thought  may  be  felt 
and  expressed. 

There  is  no  doubt  that  clearness  of  thought  is  often 
greatly  obscured  by  the  medium  of  language.  Words  come 
to  acquire  strange  twists  and  turns  which  are  productive  of 
much  misunderstanding  and  error.  It  is  the  office  of  the 
logical  mind  to  determine  the  meaning  of  words,  and  to  use 
the  word  which  most  precisely  and  adequately  expresses  the 
thought.  Obscurity  in  the  use  of  language,  however,  may 
usually  be  traced  to  obscurity  in  thought.  Clear  thinking 
will  always  find  a medium  of  clear  expression. 


CHAPTER  III 


THE  JUDGMENT 

The  essential  function  of  the  judgment  is  to  give  definite- 
ness to  the  concept.  When  the  concept  appears  in  thought, 
it  is  never  as  a complete  element  in  itself,  but  it  is  always 
as  a constitutive  element  of  a judgment.  The  concept 
exercises  no  more  independent  a function  apart  from  the 
judgment  than  does  the  sap  separated  from  the  tree  whose 
entire  structure  it  permeates.  If  we  attempt  to  hold  the 
concept  in  the  focus  of  thought,  it  will  always  appear 
elusive  and  indefinite.  It  becomes  definite  only  as  it  sug- 
gests some  judgment,  or  it  may  be  a series  of  judgments  of 
which  it  serves  to  form  the  basal  element.  We  may  seem 
at  times  to  hold  the  concept  before  the  mind  as  a naked, 
unattached  idea ; but  it  is  a barely  momentary  result  which 
is  reached.  The  concept  maintains  such  a shadowy  form, 
only  so  long  as  we  do  not  concentrate  our  thought  upon  it. 
As  soon  as  it  becomes  in  any  sense  an  object  of  thought,  it 
challenges  some  assertion  either  concerning  its  nature,  or  its 
relations  to  other  concepts  in  our  general  body  of  knowledge. 
If  we  make  a list  of  various  concepts,  such  as  iron,  educa- 
tion, freedom,  army,  horse,  bird,  fern,  and  so  on,  the  eye 
rapidly  traverses  such  a list,  instantly  recognizing  the  mean- 
ing of  each  word,  as  it  occurs,  and  immediately  passing  on 
to  the  next.  But  in  such  a process  we  have  not  really  taken 
these  various  concepts  into  our  thought.  There  has  been 
merely  a series  of  mental  reactions  in  the  recognition  of  the 
meaning  of  word  symbols.  Such  a recognition  is  nothing 
more  than  the  vague  sense  of  familiarity  which  the  several 
words  are  capable  of  arousing.  If,  however,  an  unfamiliar 

25 


26 


DEDUCTIVE  LOGIC 


word  should  appear  in  such  a list,  it  would  immediately 
give  us  pause;  we  would  begin  to  think  about  it,  to  turn  it 
over  in  our  minds,  endeavoring  to  discover  its  general  nature 
and  the  relations  which  it  sustains  to  our  other  concepts. 
This  would  at  once  give  us  a series  of  judgments.  Or  if  any 
one  of  the  suggested  words  should  elicit  any  special  interest 
on  our  part,  the  various  processes  of  thought  would  be  found 
to  react  upon  it  in  such  a manner  as  again  to  yield  a num- 
ber of  judgments.  Thus  if  we  allow  our  thought  to  dwell 
upon  such  an  idea  as  that  of  education  with  something  more 
than  a mere  passing  recognition  of  a familiar  word,  then  we 
at  once  find  ourselves  constructing  some  definite  assertions 
concerning  this  idea,  as  to  its  general  nature,  its  various 
forms,  its  methods  and  scope,  and  the  fundamental  princi- 
ples which  underlie  its  essential  significance.  Whenever  a 
concept  swings  into  the  focus  of  thought,  it  at  once  forms  a 
centre  whence  radiates  a series  of  judgments.  The  judg- 
ment may  be  defined,  therefore,  as  a concept  which  is  ren- 
dered definite  through  some  assertion  concerning  it.  The 
concept  is  a potential  judgment,  or  rather  it  is  the  potential 
of  many  judgments  which  are  implicitly  contained  in  it. 
The  judgment  is  the  concept  in  its  unfolded  form.  The 
concept,  moreover,  may  be  regarded  as  an  unstable  com- 
pound which  through  the  barest  contact  of  thought  sepa- 
rates into  its  elemental  parts  and  relations  expressed  in  the 
form  of  judgments. 

There  are  two  ways  by  which  we  may  render  any  concept 
definite  through  assertion,  thus  producing  two  general  types 
of  judgment. 

1.  The  concept  may  be  referred  to  another  concept  which 
forms  an  essential  element  in  its  constitution,  or  else  to  one 
which  sustains  some  essential  relation  to  it.  Thus  we  may 
have  the  judgment  as  follows : The  constitution  of  a nation 
embodies  the  fundamental  principles  underlying  the  judi- 
cial, legislative,  and  executive  functions  of  government. 
In  such  a judgment  we  have  the  interpretation  of  one 


THE  JUDGMENT 


27 


concept  by  others  which  enter  into  its  composition  as 
constitutive  elements  of  it. 

We  may  have  also  a judgment  which  expresses  relations 
between  concepts  as  the  following : Liberty  is  not  possible 
in  a country  where  there  is  no  respect  for  law. 

In  both  of  these  illustrations  the  judgments  relate  to  our 
knowledge  in  general. 

2.  A concept,  however,  may  be  made  definite  by  a reference 
to  some  particular  instance  which  illustrates  it,  or  a particu- 
lar instance  in  turn  may  be  referred  to  a concept  which  in- 
terprets it.  Thus  the  concept  of  philanthropy  may  be  made 
clearer  and  more  definite  by  a reference  to  certain  specific 
persons  and  their  deeds ; and  on  the  other  hand  a special 
case,  as  a peculiar  light  in  the  northern  sky,  may  be  explained 
by  a reference  to  a familiar  concept  which  serves  to  interpret 
it,  such  as  the  aurora  borealis.  Under  this  head  of  a refer- 
ence of  the  particular  experience  to  its  corresponding  univer- 
sal, we  have  the  great  body  of  our  judgments  of  identification 
or  recognition,  — such  as,  This  plant  is  a fringed  orchis, 
or  That  is  a red-winged  blackbird,  or  That  substance  is  com- 
bustible. In  these  cases,  the  particular  instance  is  referred 
to  the  appropriate  class  or  group  within  which  it  naturally 
falls,  or  to  a general  attribute  which  characterizes  it. 

Of  the  two  forms  of  judgment,  thus  outlined,  the  former 
represents  some  phase  of  our  knowledge  in  general ; the  lat- 
ter, the  application  of  some  phase  of  our  general  knowledge 
to  some  special  case. 

Whether  the  judgment  consists  of  the  characterization  of 
our  knowledge  in  general,  or  the  interpretation  of  a particu- 
lar experience  by  means  of  our  general  knowledge,  it  remains 
true  that  in  either  case  the  judgment  itself  must  rest  upon 
a sound  basis  of  reality.  A judgment  which  cannot  show 
some  basis  of  reality  upon  which  it  rests  is  a judgment  in 
name  only.  It  may  be  a fancy,  a dream,  a query,  a hope,  but 
it  is  not  a judgment.  In  this  particular  respect,  the  judg- 
ment may  be  defined  as  the  reference  of  a concept  to  reality. 


28 


DEDUCTIVE  LOGIC 


This  is  more  obvious  in  the  second  form  of  judgment,  where 
there  is  a reference  of  a particular  experience  to  a concept, 
for  in  this  case  the  reality  which  underlies  the  particular 
experience  in  question  furnishes  the  evident  basis  of  reality 
to  the  judgment  itself.  Thus  if  one  should  say,  That  is  the 
wreck  of  a sailing  vessel,  then  the  actual  object  of  perception 
evidencing  its  own  reality  to  the  senses  is  to  be  regarded  as 
referred  to  the  general  concept,  a wreck  of  a sailing  vessel, 
which  thus  identifies  and  explains  it. 

It  is  well  to  remark  in  this  connection  that  every  object 
of  perception  evidences  its  own  reality  to  the  senses,  and 
this  sense  of  reality  attaching  to  an  object  is  as  definite  and 
as  clear  a quality  of  the  object  as  its  form,  size,  color,  or  any 
of  its  various  properties  and  activities. 

This  attribute  of  reality  must  be  regarded  as  a simple, 
unanalyzable  element  of  consciousness  which  is  immediately 
given  and  attested  in  the  very  process  of  perception  itself. 

The  reference  to  reality  in  the  first  kind  of  judgment  — 
that  is,  a judgment  which  relates  to  our  knowledge  in 
general  — is  not  so  patent ; but  nevertheless  the  reality  is 
present  as  an  unseen  but  secure  foundation  for  the  truth 
of  the  judgment.  In  this  first  form  of  judgment  wherein 
one  universal  idea  is  related  to  another  universal  idea, 
where  do  we  find  any  basis  of  reality  ? If  one  idea  can  be 
explained  by  another  idea,  in  that  very  process  it  would 
seem  that  we  had  swung  clear  of  reality  altogether.  This  is 
not  so,  however.  Take  the  judgment,  The  collie  is  an  excel- 
lent sheep-dog ; here  the  reference  to  reality  is  not  direct, 
it  is  true,  but  it  is  indirect.  These  concepts,  collie  and 
sheep-dog,  have  their  origin  in  a series  of  perceptual  experi- 
ences, and  whatever  reality  may  lie  at  the  basis  of  the 
percepts  is  conserved  in  the  concepts  which  emerge  from 
them. 

Conceptual  reality  is  based  upon  perceptual  reality. 
The  concept  is  real  in  the  sense  that  it  traces  its  origin  to 
the  several  concrete  instances  whose  reality  basis  is  dis- 


THE  JUDGMENT 


29 


closed  in  perception.  When  the  latter  is  wanting,  the 
possibility  of  the  reference  of  the  concept  to  reality  is  at 
once  removed.  Thus  we  may  have  an  assertion  which  has 
the  form  but  lacks  the  substance  of  a genuine  judgment, 
such  as  the  following:  The  Centaur  is  an  animal  which 
has  the  body  of  a horse  with  the  head  and  shoulders  of  a 
man.  Here  is  a concept,  standing  as  the  subject  of  a judg- 
ment, which  can  lay  claim  to  no  perceptual  ancestry  in  our 
experience.  We  can  form  a clear  mental  picture  of  it ; it 
can  even  be  rendered  intelligible  to  the  understanding  of  a 
child ; but  there  is  no  real  experience  at  the  root  of  the  idea, 
and  therefore  it  is  nothing  but  a spectral  form  of  a judg- 
ment. Every  true  concept  in  distinction  from  a pseudo- 
concept, such  as  that  of  a Centaur,  or  a Jabberwock,  and  the 
like,  is  referable  to  some  real  experience  in  much  the  same 
way  as  the  genuine  dollar  note  may  be  referred  to  the  gold 
coin  which  it  represents  and  by  which  it  is  redeemable. 
The  counterfeit  note  presents  the  same  general  appearance 
as  the  genuine,  but  it  has  a different  history,  and  must  be 
traced  to  another  origin  which  is  of  such  a nature  as  to 
render  it  base  and  valueless. 

There  is,  however,  a certain  phase  of  reality  which  char- 
acterizes many  of  our  judgments,  and  which  underlies  the 
very  processes  of  judgment  themselves,  but  has  no  origin  in 
perception.  This  is  the  reality  which  is  discovered  in  the 
very  nature  of  thought  itself.  It  is  essentially  a thought 
reality,  and  as  such  we  become  aware  of  it  quite  indepen- 
dently of  any  particular  experience,  and  only  by  it  indeed 
is  our  experience  rendered  intelligible.  This  kind  of  reality 
is  illustrated  in  those  self-evident  truths  which  are  the  com- 
mon possession  of  all  rational  beings,  such  as  the  axioms  of 
geometry,  the  principle  of  universal  causation,  the  appreci- 
ative judgments  of  moral  worth  or  aesthetic  value.  Such 
judgments  are  given  as  examples  of  a large  group  of  judg- 
ments which  evidently  imply  as  their  basis  a form  of  reality 
which  cannot  be  traced  to  an  origin  in  mere  perception. 


30 


DEDUCTIVE  LOGIC 


There  is,  of  course,  that  school  in  philosophy  which  denies 
the  possibility  of  any  reality  of  this  kind,  but  insists  that 
all  forms  of  reality  whatsoever,  when  completely  analyzed, 
will  reveal  an  ultimate  origin  in  experience,  and  that  the 
so-called  intuitive  truths  have  had  their  beginnings  in  con- 
sciousness at  the  earliest  stages  in  human  development,  and 
have  been  transmitted  through  many  generations,  attaining 
in  each  generation  more  complete  expression,  and  more 
exact  formulation ; consequently  for  us  they  appear  in 
thought  as  judgments  which  seem  to  be  self-attested  and 
to  have  no  origin  in  our  particular  experiences.  In  the 
present  discussion  as  to  the  nature  of  the  reality  which 
underlies  our  judgments,  this  question  has  no  direct  bear- 
ing. We  find  in  our  consciousness  certain  judgments  which, 
for  us,  at  least,  whatever  their  remote  origin  may  be,  ap- 
pear as  intuitive  truths  evidencing  their  own  reality  with  a 
compulsion  of  thought  quite  as  irresistible  as  that  which 
attests  the  reality  of  any  object  which  we  may  see,  or  hear, 
or  touch. 

These  forms  of  reality  whether  attested  by  perception  or 
by  the  necessity  of  thought  itself  have  this  in  common,  — 
they  present  themselves  to  consciousness  in  such  a manner 
that  we  are  constrained  to  yield  them  a permanent  and 
constant  recognition.  To  refuse  a place  to  them  in  thought 
would  mean  the  denial  of  our  intellectual  integrity.  Reality, 
as  regards  its  significance  for  logic,  may  be  defined  as  that 
which  we  are  constrained  to  think.  The  real  compels  our 
thought.  The  dream  or  fancy  can  be  dispelled  by  the  wak- 
ing consciousness  or  the  commanding  will.  Not  so,  how- 
ever, with  the  real  object  of  perception,  or  the  necessary 
implications  of  thought.  The  ghost  is  laid  by  the  reassuring 
judgments  of  common  sense,  but  not  the  lightning,  the 
thunder,  the  storm  which  have  overtaken  us.  The  child’s 
world  is  one  in  which,  there  is  no  sharp  distinction  between 
fact  and  fancy ; especially  is  this  true  with  the  child’s  world 
of  play.  But  contact  with  the  world  of  growing  knowledge 


THE  JUDGMENT 


31 


brings  many  disillusions  and  the  reduction  of  many  cher- 
ished fancies  to  the  impossible  and  absurd. 

It  is  not  strictly  a question  of  logic,  — this  question  con- 
cerning the  ultimate  nature  of  reality.  It  is  essentially  a 
question  of  metaphysics,  for  metaphysics  has  primarily  to 
do  with  the  ultimate  nature  of  things,  — of  time,  of  space, 
of  causation,  of  God,  man,  and  the  world,  and  therefore  of 
the  ultimate  nature  of  the  reality  itself  which  underlies 
these  various  manifestations  of  it.  The  special  question 
which  metaphysics  puts  is  this : Does  our  knowledge  of 
the  world  represent  it  really  as  it  is  ? May  not  reality  be 
very  different  from  that  which  it  appears  to  be  in  my  per- 
ceptions ? Are  the  sea,  the  sky,  the  wood,  portrayed  in 
my  thought  with  an  exact  correspondence  to  the  reality 
which  constitutes  them  what  they  are  ? It  is  evident  that 
there  is  here  room  for  much  discussion,  for  much  difference 
of  opinion,  and  for  much  confusion  of  thought  as  well.  But 
logic  is  satisfied  from  its  point  of  view,  if  there  is  assurance 
that  in  the  body  of  knowledge  which  represents  our  world 
as  we  conceive  it  there  are  elements  which  maintain  a con- 
stant character,  and  that  whatever  we  come  to  think  about 
them  is  due  to  a necessity  which  underlies  their  essential 
nature.  Logic  therefore  is  not  concerned  with  the  ultimate 
nature  of  reality,  but  it  does  demand  as  the  basis  of  all 
knowledge  certain  elements  which  are  grounded  in  neces- 
sity and  admit  of  a constant  reference  in  thought. 

Moreover,  that  which  appears  to  the  individual  as  a nec- 
essary experience,  a necessary  truth,  or  a necessary  demon- 
stration receives  constantly  through  intercourse  with  one’s 
fellow-men  a social  confirmation  and  verification.  We  find 
for  the  most  part  that  our  judgments  run  parallel  to  those 
of  the  generality  of  mankind.  What  we  think,  other  men 
think.  What  is  true  for  me,  I believe  is  true  for  you  also. 
The  debatable  area  of  conflicting  opinion  is  to  be  regarded 
as  knowledge  in  the  making.  Questions  which  divided 
men’s  minds  a generation  or  two  ago  are  many  of  them  now 


32 


DEDUCTIVE  LOGIC 


settled,  and  the  results  formulated  in  universally  accepted 
judgments.  Even  where  there  may  remain  an  outstanding 
difference  of  opinion,  there  is  always  some  common  ground 
of  necessity  which  is  recognized;  and  the  lack  of  agree- 
ment is  due  to  the  fact,  not  that  the  basis  of  our  knowledge 
is  uncertain  and  shifting,  but  that  human  judgment  is 
fallible,  owing  to  the  limitations  of  experience,  the  want  of 
insight,  the  presence  of  prejudice,  or  the  undue  submission 
to  authority.  All  these  disturbing  elements  enter  into  the 
processes  of  thought  and  cause  perturbations  of  judgment. 
In  spite  however  of  such  disagreements,  the  presence  of 
an  underlying  necessity  as  the  basis  of  knowledge  is  at- 
tested and  sealed  by  the  general  agreement  of  our  judg- 
ments with  those  of  our  fellows.  The  communication  of 
thought,  the  communal  interests  and  activities,  the  indus- 
trial and  social  faith  which  is  preserved  between  man  and 
man,  the  laws  both  written  and  unwritten  which  command 
respect  and  obedience,  the  universally  recognized  standards 
of  civilized  life,  all  attest  a common  recognition  of  one  and 
the  same  element  of  necessity,  and  a common  interpre- 
tation of  the  many  phases  of  its  manifestation. 

The  difference  between  the  man  who  is  sane  and  one  who 
is  not  lies  in  the  absence  of  this  social  factor  of  agreeing 
judgments.  With  the  insane  mind  there  is  a feeling  of 
necessity  which,  however,  is  without  foundation.  The  world 
in  which  he  lives  and  moves  and  has  his  being  is  for  him 
a necessary  world.  But  in  it  he  dwells  alone.  No  one  else 
can  enter  it,  or  understand  his  view  of  it.  He  believes  that 
he  is  Julius  Csesar,  or  Napoleon,  and  it  may  be  consistently 
thinks  and  acts  in  that  character.  But  for  him  there  is  no 
fellowship  in  thought,  for  his  experiences  are  not  believed 
and  his  judgments  stand  in  conflict  with  those  of  all  the 
rest  of  mankind. 

It  is  incumbent  upon  us,  therefore,  as  logical  beings,  to 
make  sure  of  the  basis  of  reality  which  we  believe  under- 
lies our  judgments.  In  the  investigation  of  any  subject 


THE  JUDGMENT 


33 


concerning  which  we  regard  ourselves  entitled  to  a judg- 
ment, not  only  should  we  seek  as  wide  a range  of  observa- 
tion as  is  possible  concerning  the  facts  upon  which  we 
found  the  judgment,  but  we  should  acquaint  ourselves  also 
with  what  other  men  have  thought  and  have  written  upon 
the  subject.  This  is  to  be  done,  not  that  we  may  slavishly 
acquiesce  in  their  judgments,  but  that  by  a critical  exami- 
nation of  all  that  is  known  and  reported  we  may  be  the 
better  able  to  defend  our  own  position,  or  the  more  reason- 
ably to  modify  or  to  abandon  it  as  the  case  may  be. 

We  come  now  to  discuss  the  relation  of  the  judgment  as 
a form  of  thought  to  its  corresponding  expression  by  means 
of  language.  The  judgment  expressed  in  language  is  known 
as  a proposition.  The  grammatical  form  of  a proposition 
consists  of  subject,  predicate,  and  copula.  The  copula  is 
some  form  of  the  verb  “ to  be  ” either  expressed  or  implied. 
It  is  always  implied  in  any  verb  which  may  appear  in  a 
proposition.  Thus  the  proposition,  He  rows  a boat,  is  equiv- 
alent to  the  proposition,  He  is  rowing  a boat ; wherein  the 
verb  “ to  row  ” breaks  up  into  the  participle  of  the  verb  com- 
bined with  the  auxiliary  verb  “ to  be.”  This  can  occur  with 
any  verb  whatsoever,  and  therefore  in  any  verb  there  is  im- 
plied some  form  of  the  verb  “ to  be  ” ; consequently  every 
proposition  may  be  regarded  as  composed  of  subject,  predi- 
cate, and  copula. 

The  logical  function  of  these  three  parts  of  speech  needs 
some  further  exposition.  In  the  first  place,  there  is  a dis- 
tinction between  logical  subject  and  predicate  on  the  one 
hand,  and  grammatical  subject  and  predicate  on  the  other. 
The  logical  subject  of  every  proposition  is  some  phase  of 
reality  ; the  logical  predicate  is  always  the  significant  idea 
which  the  judgment  contains  applied  to  this  phase  of  reality 
in  order  to  characterize  or  interpret  it.  The  judgment  in 
this  connection  may  be  defined  as  the  interpretation  of  some 
phase  of  reality  by  means  of  some  universal  idea.  The  reality 
is  the  logical  subject ; the  universal  idea  interpreting  it  is  the 


34 


DEDUCTIVE  LOGIC 


logical  predicate.  This  statement  may  be  illustrated  as  fol- 
lows : Let  us  take  a judgment  of  the  type  in  which  a partic- 
ular experience  is  interpreted  by  means  of  a concept, — This 
is  an  excellent  essay  on  the  labor  question.  Here  the  sub- 
ject, denoted  by  the  demonstrative  adjective  “this,”  refers 
directly  to  a point  of  the  world  of  reality,  evident  to  the 
senses,  something  visible  and  tangible ; the  predicate  is  the 
complex  concept,  “an  excellent  essay  on  the  labor  question,” 
which  is  asserted  of  the  subject  in  question.  The  thought 
form  interprets  the  perceived  reality  simply.  In  this  type 
of  judgments,  the  logical  subject  and  predicate  coincide 
with  the  grammatical  subject  and  predicate. 

In  the  other  form  of  judgment  which  is  a characterization 
of  some  phase  of  our  knowledge  in  general,  the  logical  sub- 
ject and  predicate  do  not  coincide  with  the  grammatical 
subject  and  predicate.  For  instance,  let  us  consider  the 
proposition,  — All  permanent  reforms  emanate  from  the 
people.  Here  the  grammatical  subject  is  “ all  permanent 
reforms  ” ; the  grammatical  predicate  is  that  they  “ emanate 
from  the  people.” 

Now  it  is  the  function  of  the  copula  to  fuse  together  the 
grammatical  subject  and  predicate  into  one  idea  which  forms 
the  heart  of  the  judgment  and  its  real  logical  predicate. 
For  while  language  separates  the  grammatical  subject  and 
predicate,  the  two  must  be  conceived  as  merely  parts  of  one 
and  the  same  idea  in  thought.  The  grammatical  predicate, 
in  this  case  the  phrase  “ emanate  from  the  people,”  is  an 
essential  characteristic  of  the  grammatical  subject,  “ perma- 
nent  reform  ” ; together  they  form  but  a single  idea,  namely, 
a permanent  reform  emanating  from  the  people.  This  is 
the  logical  predicate  which  is  affirmed  of  this  particular 
phase  ot  that  reality  which  lies  at  the  basis  of  every  true 
judgment,  and  though  not  expressed  in  the  grammatical 
form  of  the  proposition  nevertheless  constitutes  its  logical 
subject.  The  logical  significance  of  this  judgment,  if  ex- 
plicitly expressed,  would  be  somewhat  as  follows : The 


THE  JUDGMENT 


35 


world  of  reality  as  I am  constrained  to  regard  it  is  such 
as  to  necessitate  that  all  permanent  reforms  should  emanate 
from  the  people.  And  this  may  serve  as  a type  of  all  our 
universal  judgments ; they  affirm  of  some  phase  of  reality 
the  central  idea  which  constitutes  the  heart  of  the  judgment 
itself.  A false  judgment  contains  at  its  heart  a central 
idea  to  which  there  is  no  corresponding  subject  in  the  real 
world  of  knowledge. 

When  we  come  to  put  into  words  the  single  idea  which 
always  lies  at  the  root  of  the  essential  unity  of  the  judg- 
ment, why  do  we  separate  this  unitary  idea  into  two,  the 
grammatical  subject  and  the  grammatical  predicate?  The 
reason  is  that  while  the  idea  in  question  represents  a single 
unified  thought,  it  is  nevertheless  complex  and  capable  of 
an  analysis  into  two  component  elements,  one  the  grammati- 
cal subject  and  the  other  the  grammatical  predicate.  Judg- 
ment is  a process  which  consists  in  relating  one  phase  of 
an  idea  to  another  phase  of  the  same  idea,  and  in  rendering 
evident  the  unity  which  underlies  them.  The  grammatical 
subject  forms  one  of  these  phases;  the  grammatical  predi- 
cate forms  the  other.  The  copula  serves  to  bring  them  to- 
gether and  to  affirm  their  unity.  Thus  every  proposition 
is  the  expression  of  the  complementary  processes  of  analysis 
and  synthesis  ; the  analysis  is  expressed  by  the  grammatical 
subject  and  predicate,  the  synthesis  by  the  force  of  the 
copula  whose  function  it  is  to  blend  the  two  into  one  logical 
idea  which  forms  the  very  essence  of  the  judgment  itself. 

In  connection  with  this  discussion  of  the  relation  of 
language  to  thought,  it  would  be  well  to  call  attention  to 
the  meaning  of  the  word  term  in  logic.  A term  is  any  word 
or  combination  of  words  considered  as  a part  of  a proposition, 
that  is,  as  subject  or  predicate.  The  term,  therefore,  is  the 
expression  in  language  of  the  concept  as  an  integral  part 
of  the  judgment. 


CHAPTER  IV 


THE  UNIVERSAL  JUDGMENT 

Judgments,  as  we  have  seen,  are  of  two  kinds.  The 
first  represents  some  one  or  other  of  the  many  phases  of 
our  general  knowledge.  The  second  serves  to  interpret  the 
special  case  in  the  light  of  general  knowledge.  The  first 
type  is  known  as  the  universal  judgment.  Our  general 
body  of  knowledge  is  composed  of  judgments  of  this  kind, 
and  if  they  are  to  prove  serviceable  in  the  interpretation  of 
special  cases  as  they  arise,  they  must  together  form  an 
orderly  system.  The  concepts  which  form  the  constitutive 
elements  of  these  judgments  are  all  interrelated.  Every 
concept  represents  a point  whence  radiate  lines  of  connection 
with  many  other  concepts.  It  is  impossible  to  frame  a 
judgment  which  shall  contain  a concept  out  of  all  relation 
to  other  concepts. 

If,  for  instance,  we  analyze  the  full  significance  of  the 
abstract  concept  of  redness,  we  at  once  relate  it  in  our 
thought  to  the  general  color  system,  which  in  turn  we  refer 
to  light  as  its  source.  The  idea  of  light  at  once  suggests  the 
ether  vibrations  which  affect  the  retina  of  the  eye,  and  this, 
in  turn,  the  transmission  of  the  physiological  disturbance 
which  occurs  in  the  retina  to  the  optic  lobes  of  the  brain, 
and  then  the  resultant  reaction  which  is  attended  by  the 
consciousness  of  a color  sensation.  Thus  the  examination 
of  any  concept  will  reveal  an  indefinite  number  of  relations 
extending  into  the  general  body  of  our  knowledge.  Their 
formulation  gives  rise  to  a series  of  descriptive  judgments. 
Our  knowledge  therefore  so  far  as  it  is  worthy  the  name 

36 


THE  UNIVERSAL  JUDGMENT 


37 


of  knowledge,  represents  an  organized  system  of  relations. 
Moreover,  there  are  certain  general  principles  which  underlie 
the  process  of  organizing  the  various  elements  of  knowledge. 
These  principles  pertain  to  the  very  nature  of  thought  itself, 
and  man  has  universally  employed  them  in  constructing 
his  world  of  knowledge.  These  fundamental  principles  are 
called  the  categories  of  thought.  They  indicate  the  various 
possible  ways  by  which  conceptual  elements  are  related  so 
as  to  form  the  unitary  idea  which  lies  at  the  basis  of  the 
judgment. 

As  given  by  Aristotle,  the  categories,  ten  in  number,  are 
as  follows : — 

e 6.  7 rore  time 


Thus  any  concept  whatever  may  be  regarded  from  one  or 
more  of  these  points  of  view,  — as  to  its  substance,  what  it 
is ; as  to  its  various  attributes,  its  dimensions  and  weight ; 
the  relations  which  it  sustains ; its  space  and  time  condi- 
tions ; its  relative  position  as  regards  its  surroundings ; as 
to  what  it  may  possess ; as  to  how  it  acts ; and  how  it  is 
acted  upon.  The  list  exhausts  the  possibilities  of  descrip- 
tion. The  word  KarrjyopLa,  as  used  by  Aristotle,  means  as- 
sertion or  predication.  The  table  of  the  categories  presents 
the  possibilities  of  the  various  kinds  of  assertion.  We  have 
seen,  moreover,  that  a judgment  is  a process  essentially  of 
assertion.  The  categories  therefore  give  us  the  possible 
varieties  of  judgment.  These  categories  suggest  a cor- 
responding division  of  words  into  the  various  parts  of 
speech.  The  substance  corresponds  to  the  noun  ; quantity, 
quality,  and  relation  to  the  adjective  ; place,  time,  and  pos- 
ture to  the  adverb;  having,  acting,  and  being  acted  upon  to 
the  verb.  Thus  we  have  outlined  the  possibilities,  not  only 


5.  nov  place 


7.  KelcrOtu  posture  or  attitude 

8.  exetv  having 

9.  7rot£tv  acting 

10.  7racrx£iv  being  acted  upon 


38 


DEDUCTIVE  LOGIC 


of  thought  relations,  but  of  the  expression  of  the  same  in 
language. 

There  are,  moreover,  certain  considerations  in  reference  to 
these  categories  which  enable  us  to  coordinate  the  various 
portions  of  our  knowledge  so  as  to  form  out  of  them  a system 
which  shall  show  unity  and  order.  These  considerations 
are  as  follows  : — 

The  first  category  is  substance ; the  other  nine  categories 
give  the  various  kinds  of  possible  attributes  which  together 
serve  to  determine  the  essential  nature  of  any  concept,  that 
is,  its  substance,  this  first  of  the  categories.  Of  these  various 
attributes,  some  will  be  common  to  a number  of  concepts. 
This  will  enable  us  to  group  similar  concepts  together. 
Other  attributes  will  be  unique  as  regards  some  particular 
concept.  They  will  serve  as  a distinguishing  mark  of  the 
concept  in  question.  Others  again  appear  in  certain  special 
instances  of  a concept,  but  not  in  all.  This  serves  to  mark 
the  distinction  between  constant  and  variable  attributes,  a 
distinction  which  is  exceedingly  valuable  from  the  stand- 
point of  logic ; for  it  draws  the  line  between  attributes  and 
relations  which  have  a universal  validity  and  those  which 
are  shifting  and  uncertain. 

The  above  considerations  are  formulated  under  five  tech- 
nical terms,  known  in  logic  as  the  Heads  of  Predicables ; 
that  is,  the  various  ways  in  which  a predicate  given  by  any 
one  of  the  categories  may  be  affirmed  of  a subject,  or  of  the 
concept  regarded  in  the  light  of  the  first  category,  substance. 
These  terms  are  as  follows : — 

1.  Genus. 

2.  Species. 

3.  Property. 

4.  Differentia,  or  Specific  Difference. 

5.  Accident.1 

1 Aristotle  gives  but  four  forms,  including  “species  ’’under  “genus,” 
and  instead  of  “ differentia,”  giving  “ definition.” 


THE  UNIVERSAL  JUDGMENT 


39 


They  are  the  Heads  of  Predicables,  as  given  by  Porphyry 
(230-300  a.d.)  in  his  Introduction  to  Aristotle’s  Treatise  on 
the  Categories. 

Genus  and  species  are  relative  terms  and  can  best  be 
defined  together.  The  genus  is  always  a larger  class  which 
embraces  two  or  more  smaller  classes  under  it  by  reason  of 
their  common  attributes. 

The  species  is  any  one  of  the  smaller  classes  which  is 
embraced  under  the  genus. 

The  property  is  an  attribute  which  pertains  to  the  very 
nature  of  the  concept  itself. 

The  differentia  is  that  particular  property  which  serves  to 
distinguish  a given  species  from  all  others  belonging  to  the 
same  genus. 

The  accident  is  an  attribute  which  does  not  pertain  to  the 
essential  nature  of  the  concept,  and  therefore  may  be  present 
or  absent  without  affecting  the  integrity  of  the  concept  in 
question. 

These  distinctions  may  be  illustrated  in  the  following 
proposition : — 

Democracy  ( species ) is  a form  of  government  (genus)  in 
which  the  supreme  power  is  vested  in  the  people  (differ- 
entia) ; it  is  attended  by  certain  dangers  due  to  the  dissipa- 
tion of  responsibility  (property)  ; it  is  regarded  in  the 
United  States  by  some  as  a proved  success,  by  others  as 
still  in  the  experimental  stage  (accident). 

The  several  species  under  one  genus  are  called  cognate 
species. 

A generic  property  is  one  which  grows  out  of  the  idea 
represented  by  the  genus,  and  which  therefore  all  cognate 
species  have  in  common. 

A specific  property  is  one  which  grows  out  of  the  idea 
represented  by  the  differentia,  and  belongs  therefore  only 
to  one  of  a number  of  cognate  species. 

Genus  and  species,  being  relative  terms,  a concept  may 
be  regarded  as  a species  relative  to  a genus  which  embraces 


40 


DEDUCTIVE  LOGIC 


it,  but  a genus  relative  to  the  various  species  which  it 
embraces. 

There  is  however  the  summum  genus,  which  can  be  re- 
ferred to  no  larger  class,  and  also  the  infima  species,  which 
cannot  be  broken  up  into  any  smaller  classes. 

In  the  light  of  these  various  distinctions,  we  may  group 
our  judgments  in  several  classes,  according  to  the  dif- 
ferent ways  by  which  the  concepts  in  these  judgments  are 
related. 

1.  The  possibility  of  referring  a species  as  a subject  to 
its  corresponding  genus  as  a predicate ; e.g.  The  purple 
martin  is  a swallow. 

2.  The  possibility  of  referring  a genus  as  a subject  to  the 
various  species  under  it  which  together  form  the  predicate  ; 
e.g.  The  swallow  may  be  a purple  martin,  a barn  swallow,  a 
cliff  swallow,  etc. 

3.  The  possibility  of  describing  any  species  as  a subject 
by  one  or  more  of  its  properties  as  a predicate ; e.g.  Cast 
iron  has  a specific  gravity  of  7.20. 

The  special  case  of  this  group  is  where  the  property 
chosen  is  the  differentia  of  the  species ; e.g.  Capital  is 
wealth  which  is  actually  used  for  producing  more  wealth. 

4.  The  possibility  of  describing  a concept  by  its  accident ; 
e.g.  Some  animals  can  swim. 

A judgment  in  this  latter  form  is  known  as  a particular 
judgment.  It  is  not  a statement  in  terms  of  a universal ; 
neither  indeed  can  it  be  as  long  as  the  predicate  is  an  ac- 
cident of  the  concept  which  appears  as  subject. 

It  must  not  be  overlooked,  however,  that  any  predicate 
which  is  an  accident  may  be  raised  to  the  higher  level  of  a 
property  in  reference  to  any  concept,  provided  that  concept 
is  only  more  specifically  limited.  Thus  if  we  change  the 
above  proposition  by  inserting  the  limiting  adjective  “ web- 
footed,” the  predicate  at  once  becomes  the  property  of  the 
subject  thus  limited,  and  instead  of  a particular  judgment, 
as  in  the  former  case,  we  now  have  the  universal  judgment, 


THE  UNIVERSAL  JUDGMENT 


41 


— All  web-footed  animals  can  swim.  In  general  it  may  be 
said  that  an  accident  of  any  species  always  becomes  the 
property  of  that  same  species  under  certain  definite  restric- 
tions. Every  accident,  therefore,  is  a potential  property. 
To  call  any  attribute  of  a species  an  accident  is  a confes- 
sion of  ignorance,  for  if  we  only  know  the  corresponding 
limitation  of  the  species  in  question,  the  accident  at  once  is 
transformed  into  a property. 

If  our  knowledge  were  perfect,  we  should  be  able  to 
explain  all  accidental  variations,  even  the  most  minute  and 
seemingly  insignificant.  Each  so-called  accident  could  then 
be  regarded  as  a property  and  be  referred  to  some  constant 
element  within  the  nature  of  the  concept  itself  as  its  cause. 
Every  variation  in  nature,  whether  of  color,  or  form,  or 
peculiarities  of  habit  and  disposition,  has  a good  and  suffi- 
cient reason  why  it  is  what  it  is  and  not  anything  else.  To 
call  such  variations  mere  accidents  of  a species  is  of  course 
a confession  of  ignorance.  This  leads  us  to  the  fifth  pos- 
sibility of  reference. 

5.  The  possibility  of  referring  properties  of  concepts  to 
definite  conditions  as  their  cause.  The  causal  relation  when 
expressed  or  implied  in  a judgment  not  only  renders  that 
judgment  more  definite  and  consequently  serves  to  perfect 
the  order  of  the  general  body  of  knowledge,  but  it  also 
furnishes  the  ground  for  the  judgment  itself  and  conse- 
quently serves  to  justify  it.  Take  for  instance  the  proposi- 
tion, A conic  section  formed  by  a cutting  plane  parallel 
to  the  base  of  a cone  is  always  a circle.  Here  the  circle,  as 
regards  a conic  section  in  general,  is  an  accident,  but  as 
regards  a conic  section  under  the  condition  that  the  cutting 
plane  is  parallel  to  the  base,  it  is  an  essential  property. 
The  condition  determines  the  property,  and  the  two  are 
related  as  cause  and  effect.  So,  also,  to  further  illustrate 
this  relation,  the  freezing  or  boiling  of  water  may  be  regarded 
as  accidents,  so  far  as  the  concept  of  water  in  general  is 
concerned.  They  are,  however,  properties  of  water  when 


42 


DEDUCTIVE  LOGIC 


specifically  determined  by  the  freezing  and  boiling  condi- 
tions. 

Knowledge,  therefore,  which  is  vague  and  indefinite,  gives 
rise  to  judgments  whose  predicates  are  accidents  of  the 
subject  concept.  Definite  knowledge,  on  the  other  hand, 
always  gives  rise  to  judgments  whose  predicates  are  prop- 
erties of  the  subject  concept.  The  bond  of  connection  or 
inherence  between  any  species  and  its  property  forms  the 
ground  of  the  universal  judgment. 

In  the  various  relations  which  concepts  may  sustain  to 
one  another  in  the  general  scheme  which  has  been  given, 
there  are,  in  the  main,  two  points  of  view  from  which  a 
concept  may  be  regarded,  giving  rise  to  two  different  kinds 
of  judgment.  The  one  point  of  view  is  known  as  that  of 
extension  and  the  other  that  of  intension.  The  extension 
of  a concept  refers  to  the  range  of  its  application.  The 
intension  refers  to  the  various  properties  which  constitute 
its  meaning.  The  term  denotation  is  used  as  equivalent  to 
extension;  and  connotation  as  equivalent  to  intension.  The 
term  content  is  also  used  in  much  the  same  sense  as  con- 
notation or  intension.  By  some  writers  the  terms  extension 
and  intension  are  applied  to  concepts,  while  denotation  and 
connotation  are  applied  to  terms,  the  language  symbols  of 
concepts.  In  ordinary  usage,  however,  extension  and  de- 
notation are  used  interchangeably ; so  also  intension  and 
connotation.  Two  questions  naturally  arise  in  reference  to 
any  concept : the  first,  what  is  its  meaning  ? and  the  sec- 
ond, to  what  extent  within  the  range  of  our  knowledge 
may  it  be  applied  ? It  is  obvious  that  these  two  questions 
are  mutually  dependent.  It  is  impossible  of  course,  to 
know  the  number  of  special  cases  to  which  the  concept  may 
be  applied  if  we  know  nothing  of  its  distinctive  properties; 
and,  on  the  other  hand,  we  can  know  nothing  of  the  distinc- 
tive properties  unless  we  possess  some  knowledge  of  the 
special  cases  illustrating  them. 

The  distinction  between  intension  and  extension  gives 


THE  UNIVERSAL  JUDGMENT 


43 


rise  to  two  topics  known  as  definition  and  division.  Defi- 
nition is  the  process  of  unfolding  the  connotation  of  any 
term,  and  division  is  the  process  of  unfolding  the  denotation 
of  a term ; that  is,  the  former  tells  what  it  is,  the  latter  to 
what  instances  it  may  be  applied.  These  two  processes  we 
will  now  consider  more  in  detail. 


CHAPTER  V 


DEFINITION 

Definition  is  the  process  of  unfolding  the  connotation 
of  a concept.  A statement  giving  the  complete  connota- 
tion, however,  would  be  overloaded  and  would  weigh  down 
our  thought  and  its  expression  with  a superfluous  burden. 
If  a definition  serves  to  locate  a concept  in  its  proper  region 
within  the  general  body  of  knowledge,  and  in  addition  dis- 
tinguishes it  from  all  other  cognate  concepts  which  may 
fall  within  the  same  general  area  of  thought,  then  it  may 
be  said  to  perform  its  function  satisfactorily.  The  function 
of  definition  is  expressed  by  the  following  rule : Definition 
consists  in  referring  any  concept  to  its  proximate  genus,  i.e. 
the  genus  immediately  above  it,  and  also  in  giving  its 
appropriate  differentia. 

To  define  means  to  set  limits  or  bounds.  This  rule  in- 
dicates two  defining  circles : the  first,  the  genus,  marks  the 
larger  area  within  whose  range  the  concept  belongs ; the 
second,  the  differentia,  draws  a narrower  circle  which  sepa- 
rates the  concept  within  it  from  all  others  which  lie  within 
the  outer  circle,  and  yet  outside  this  inner  circle  of  more 
exact  specification.  This  method  of  defining  is  a procedure 
which  should  always  be  followed  when  it  is  possible.  There 
are  other  modes  of  definition  which  are  less  complete,  but 
which  it  is  sometimes  necessary  to  employ,  as  will  be  shown 
later.  The  above  method,  however,  is  preferable,  as  it  alone 
can  give  what  is  known  as  the  essential  definition. 

A distinction  is  drawn  by  some  logicians  between  a real 
and  a nominal  definition.  The  real  definition  is  regarded  as 
one  which  gives  the  meaning  of  the  concept ; the  nominal, 

44 


DEFINITION 


45 


as  giving  the  meaning  of  the  term  which  is  the  language 
symbol  of  the  concept.  Some  writers,  as  Sigwart  and  Mill, 
declare  that  there  can  be  no  such  thing  as  a real  definition, 
inasmuch  as  the  process  of  defining  consists  in  unfolding 
the  meaning  of  words.  Definition,  from  this  point  of  view,  is 
merely  the  art  of  fitting  the  word  to  the  idea  which  it  repre- 
sents. It  seems  to  me,  however,  that  the  process  of  defini- 
tion must  primarily  refer  to  the  meaning  of  the  thought, 
and  only  in  a secondary  sense  to  the  meaning  of  the  word 
which  is  the  symbol  of  the  thought.  For  the  symbol  can 
have  no  meaning,  except  as  it  represents  some  thought 
behind  it.  And,  in  the  second  place,  to  define  means  to 
render  definite.  Consequently,  a definition  of  terms  presup- 
poses always  a preliminary  transformation  of  our  ideas  from 
an  indefinite  to  a definite  state  of  determination.  It  is 
thought  determination  alone  which  can  afford  a basis  for 
exact  verbal  definition.  To  draw  a line  of  distinction  be- 
tween a real  and  a nominal  definition  is  to  misunderstand 
the  relation  which  obtains  between  a symbol  and  that  which 
it  symbolizes. 

There  are  certain  rules  which  should  be  observed  in 
definition : — 

1.  The  term  defined  should  be  coextensive  with  the  defini- 
tion, neither  greater  nor  less.  The  following  is  an  example 
of  the  violation  of  this  rule:  Logic  is  a normative  science. 
Here  the  term  “ normative  science  ” is  not  coextensive  with 
“ logic,”  for  it  includes  ethics  and  aesthetics  as  well  as  logic. 

2.  The  definition  shonld  not  contain  any  superfluous 
material.  Take  the  following  definition  : — An  hallucina- 
tion is  a fancied  perception  (genus)  without  basis  of  fact 
(differentia),  and  which  indicates  an  abnormal  state  of 
consciousness.  The  latter  clause,  while  quite  true,  is  alto- 
gether superfluous.  The  definition  should  be  always  in  as 
concise  a form  as  possible. 

3.  The  definition  should  not  repeat  the  term  to  be  defined 
either  explicitly  or  implicitly.  The  violation  of  this  rule  is 


46 


DEDUCTIVE  LOGIC 


known  as  defining  in  a circle  (circulus  in  definiendo).  In  an 
examination  recently  given  the  terms  “ percept  ” and  “ con- 
cept” were  deSned  as  follows:  — A percept  is  that  which 
is  perceived.  A concept  is  that  which  is  conceived.  These 
definitions  are  incorrect  also  for  another  reason,  because 
they  contain  no  proper  genus.  Instead  of  a true  genus  to 
which  the  term  defined  is  referred  there  is  substituted  the 
indefinite  and  unsatisfactory  phrase  “ that  which.” 

Under  this  head  of  explicit  or  implicit  repetition  of  the 
term  to  be  defined  may  be  included  all  synonyms  of  the 
term  in  question.  There  is  the  following  remark  of  Hume 
which  illustrates  this.  Speaking  of  the  definition  of  the 
term  “ efficacy,”  he  says : “ I begin  with  observing  that  the 
terms  of  efficacy,  agency,  power,  force,  energy,  necessity,  con- 
nexion, and  productive  quality  are  all  nearly  synonymous ; 
and  therefore  it  is  an  absurdity  to  employ  any  one  of 
them  in  defining  the  rest.  By  this  observation  we  reject  at 
once  all  the  vulgar  definitions  which  philosophers  have  given 
of  power  and  efficacy ; and  instead  of  searching  for  the  idea 
in  these  definitions,  must  look  for  it  in  the  impressions 
from  which  it  is  originally  derived.”  1 

It  sometimes  happens  that  in  a compound  term  the  in- 
cidence of  the  definition  falls  only  upon  one  of  the  elements 
which  compose  the  compound.  In  such  a case,  the  other 
element  of  the  compound  term  may  be  repeated  in  the  defi- 
nition. Thus  the  terms,  “ vesper-sparrow,”  “ gun-metal,” 
“armored  cruiser,”  may  be  defined  by  referring  each  to  its 
appropriate  genus,  “ sparrow,”  “ metal,”  “ cruiser,”  and  then 
giving  its  corresponding  differentia. 

4 A definition  should  never  be  in  obscurer  language  than 
the  term  to  be  defined.  The  violation  of  this  rule  is  called 
“ ignotum  per  ignotius.” 

An  example  of  this  is  the  following:  A state  is  an 
ethnic  unit  which  lies  within  a geographical  unit. 

1 Hume,  A Treatise  of  Human  Nature.  Edited  by  Green  and  Grose, 
p.  451. 


DEFINITION 


47 


Sometimes,  however,  in  defining  technical  terms  it  is 
necessary  to  use  technical  words,  and  an  impression  is 
given  to  the  uninitiated  at  least  of  an  obscure  definition. 
Such  a definition  is  Herbert  Spencer’s  of  evolution.  “ Evo- 
lution is  a continuous  change  from  an  indefinite  incoherent 
homogeneity  to  a definite  coherent  heterogeneity  through 
successive  differentiations  and  integrations.”  In  this  defi- 
nition every  term  used  has  a definite  connotation  with  which 
every  student  of  the  subject  has  become  familiar,  and  there- 
fore to  such  an  one  this  definition  is  exceedingly  luminous. 

5.  A definition  should  never  contain  negative  expressions 
when  it  is  possible  to  state  it  by  means  of  the  proper  posi- 
tive terms. 

The  following  is  a violation  of  the  rule : — 

A utilitarian  is  one  who  does  not  believe  in  an  intuitional 
basis  of  morals. 

It  is  always  desirable  to  define  any  term  by  what  it  is 
rather  than  by  what  it  is  not. 

There  are  certain  terms,  however,  which  by  their  very 
nature  admit  of  a negative  definition  only.  Such  terms 
are  the  following,  — anarchist,  blindness,  unarmored  cruiser, 
supernatural,  and  the  like. 

There  are  other  forms  of  definition  which  are  substituted 
for  the  ideal  form  per  genus  et  differentiam.  Sometimes 
they  are  mere  makeshifts  at  definition,  when  one  is  ignorant 
of  the  true  genus  or  differentia;  and  often  for  some  spe- 
cial reason  they  better  serve  the  purpose  of  a satisfactory 
definition. 

They  are  as  follows : — 

1.  Definition  by  description.  When  the  genus  or  the  dif- 
ferentia is  unknown,  then  the  concept  may  be  described  by 
its  various  properties.  A person  thinks  that  he  has  dis- 
covered a new  species  of  plant.  He  is  in  doubt  as  to  its 
precise  differentia.  An  exact  definition  is  impossible.  He 
wishes,  however,  to  publish  some  account  of  it.  The  only 
course  which  is  possible  under  the  circumstances  is  to  give 


48 


DEDUCTIVE  LOGIC 


a complete  description  of  it,  especially  as  regards  those  prop- 
erties in  which  it  deviates  in  any  marked  degree  from  the 
type.  The  description  may  serve  as  a basis  for  the  discovery 
of  the  real  differentia. 

It  often  happens  when  one  begins  a new  study,  and  the 
material  he  has  to  deal  with  is  unfamiliar,  that  precise  defi- 
nitions are  impossible.  At  this  preliminary  period  descrip- 
tion must  take  the  place  of  definition.  Later  with  the 
mastery  of  the  subject  comes  the  possibility  of  framing 
satisfactory  definitions. 

2.  Definition  for  the  purpose  of  identification.  Instead  of 
the  differentia  which  may  be  a property  that  is  not  evident 
to  a surface  observation,  there  may  be  substituted  in  the 
definition  another  property  which  is  readily  observable  and 
which  serves  as  a mark  of  identification.  Thus  we  may  de- 
fine an  acid  as  a chemical  compound  which  turns  blue  litmus 
red.  It  is  not  a definition  of  an  acid,  but  it  is  a most 
convenient  formula  of  identification.  Or  we  may  define 
sassafras  as  a tree  of  the  laurel  family  whose  bark  has  an 
aromatic  odor  or  taste.  Such  formulae  are  most  valuable  as 
working  definitions.  Sometimes  the  property  which  best 
serves  as  a basis  for  identification  is  a very  insignificant 
one.  Thus  the  color  markings  of  birds,  such  as  the  white 
tail-feather  of  the  vesper-sparrow,  may  furnish  a convenient 
and  perfectly  satisfactory  basis  for  identification.  It  may 
be  that  the  peculiar  mode  of  flight  may  serve  a similar 
purpose.  In  all  such  instances  a superficial  property  is 
substituted  for  the  differentia. 

3.  The  genetic  definition,  which  refers  the  concept  to  be 
defined  to  its  origin.  The  genetic  definition,  in  giving  the 
origin  of  the  concept,  furnishes  at  the  same  time  a method 
by  which  special  instances  of  the  concept  may  be  produced, 
and  made  available  for  observation  and  experiment.  Thus 
the  genetic  definition  of  sulphuric  acid  is  given  by  the 
formula  H2S04.  Here  the  compound  is  defined  by  the  com- 
ponent elements  of  which  its  essential  nature  consists.  The 


DEFINITION 


49 


genetic  definition  of  a certain  dye  would  be  in  terms  of  the 
formula  by  means  of  which  the  dye  may  be  produced.  So 
also  all  recipes,  prescriptions,  and  methods  of  construction 
may  be  regarded  as  definitions  of  this  class.  Any  concrete 
instance  may  be  produced  at  will  by  following  the  sugges- 
tions contained  in  the  definitions.  Thus  it  is  a genetic 
definition  of  a right  cylinder  that  it  is  a solid  body  con- 
ceived as  generated  by  the  rotation  of  a rectangle  about  one 
of  its  sides  as  an  axis.  So  also  the  various  colors  of  the 
spectrum  may  be  defined  in  terms  of  the  number  of  vibra- 
tions corresponding  to  each  color. 

The  genetic  definition  is  one  which  has  always  a practical 
significance  inasmuch  as  it  furnishes  knowledge  in  such  a 
form  as  to  subserve  the  ends  of  utility.  It  not  only  tells 
us  the  meaning  of  certain  ideas,  but  it  also  indicates  how 
we  may  apply  them  in  the  arts,  the  sciences,  and  the  practi- 
cal needs  of  our  lives. 


CHAPTER  VI 


DIVISION  AND  CLASSIFICATION 

Division  is  a process  by  which  the  denotation  of  a con- 
cept is  exhibited.  The  result  is  that  form  of  judgment  in 
which  the  subject  term  represents  the  concept  regarded  as  a 
genus,  and  the  predicate  term  contains  the  several  species 
which  fall  under  it.  The  process  of  definition  always 
underlies  that  of  division,  for  we  must  know  the  differentia 
of  each  species  before  it  is  possible  to  consider  it  as  a dis- 
tinct group  under  a given  genus.  In  dividing  a concept 
into  its  appropriate  species,  one  may  proceed  in  a number  of 
different  ways  according  to  the  point  of  view  he  may  choose 
to  take.  The  point  of  view  determines  in  every  case  the 
so-called  principle  of  division  ( fundamentum  divisionis). 

Thus  we  may  divide  the  general  concept,  education,  ac- 
cording to  the  principle  of  the  progressive  stages  of  educa- 
tion regarded  as  a process,  as  primary,  secondary,  collegiate, 
university,  and  professional ; or  the  principle  chosen  may  be 
that  of  the  general  nature  of  the  course  of  studies  pursued, 
such  as  the  common  school,  academic,  scientific,  technical, 
etc. ; or  again,  the  principle  of  division  may  be  an  historical 
one,  giving  the  periods  of  ancient,  mediaeval,  and  modern 
education.  It  is  obvious  that  the  principle  of  division  will 
vary  according  to  one’s  special  interest  or  purpose.  There  is 
thus  a wide  range  of  possibility  as  regards  the  analysis  of 
our  various  concepts.  There  is  no  beaten  road  for  thought 
to  travel,  but  each  one  may  cut  out  his  own  path.  In  the 
midst  of  this  variety  of  choice,  however,  there  are  certain 
rules  which  logic  imposes  upon  the  free  play  of  thought. 
Within  the  bounds  of  these  restrictions  the  inventive  spirit 

50 


DIVISION  AND  CLASSIFICATION 


51 


may  range  at  will;  but  the  violation  of  them  brings  con- 
fusion and  inconsistency  of  thought.  The  rules  are : — 

1.  There  must  be  but  one  principle  of  division.  A 
violation  of  this  rule,  for  instance,  would  be  such  a division 
as  that  of  the  concept  “education”  into  primary,  secondary, 
collegiate,  technical,  scientific,  and  professional. 

2.  The  members  of  a division  should  be  mutually 
exclusive ; no  two  members  of  a division  should  overlap. 
The  above  example  illustrates  the  violation  of  this  rule  also. 
The  following  furnishes  another  illustration : The  division 
of  the  discontented  classes  in  society  into  socialists,  an- 
archists, nihilists,  and  populists. 

While  the  violation  of  the  first  rule  produces  overlapping 
divisions,  nevertheless  the  same  error  may  be  due  to  other 
causes  even  when  the  requirements  of  the  first  rule  are 
realized. 

3.  The  division  must  be  exhaustive.  No  possibility 
should  be  overlooked  and  omitted  from  the  division.  Thus 
if  we  divide  conduct  into  two  classes,  the  moral  and  immoral, 
the  division  is  at  fault  because  of  its  incompleteness.  There 
is  still  a third  class  which  is  omitted,  namely,  that  of  con- 
duct which  is  morally  indifferent,  and  concerning  which  it 
is  not  possible  to  affirm  that  it  is  either  moral  or  immoral. 

There  is  a particular  method  of  division  known  as  Dichot- 
omy which  provides  for  an  exhaustive  division  under  all 
circumstances.  It  consists  in  dividing  a concept  into  two 
parts,  according  to  the  presence  or  the  absence  of  a 
differentiating  attribute  which  is  chosen  as  the  principle 
of  division.  This  may  be  illustrated  by  the  so-called  “ Tree 
of  Porphyry,”  which  exhibits  a continued  division  of  that 
most  general  and  all-comprehensive  concept,  being. 


52 


DEDUCTIVE  LOGIC 


Being 


corporeal  incorporeal 


animate  inanimate 


sensible  insensible 


rational  irrational 


Plato  Aristotle  and  other  individuals 

Such  a division  is  more  curious  than  satisfactory,  for  one 
of  the  members  in  each  successive  division  is  left  indefinite, 
being  designated  by  what  it  is  not,  rather  than  by  what  it  is. 
Moreover,  if  a positive  term  is  substituted  for  the  negative, 
and  its  precise  connotation  is  attempted,  it  will  in  all 
probability  not  be  a complete  opposite  of  the  first  term  of 
the  dichotomy.  If  this  is  the  case,  the  division  itself  is  not 
complete,  for  the  dividing  of  a concept  into  two  members 
which  are  not  exact  opposites  renders  it  possible  to  inter- 
polate between  them  one  or  more  possibilities  which  do  not 
belong  to  the  one  or  the  other  of  the  extremes.  In  this  connec- 
tion it  is  necessary  to  distinguish  between  contradictory  and 
contrary  or  opposite  terms. 

Contradictory  terms  are  such  that  they  divide  the  whole 
universe  of  thought  between  them  and  admit  of  no  middle 
ground. 

Contrary  terms  stand  opposite  to  each  other  as  extremes, 
but  there  is  a possibility  of  middle  ground  between  them. 

Animate  and  inanimate  are  contradictory,  bitter  and 
sweet  are  contrary  terms. 

A dichotomous  division  requires  its  terms  to  be  related  as 
contradictories.  There  is  perhaps  no  error  in  division  which 
is  more  frequent  or  more  insidious  than  this,  of  dividing  a 


DIVISION  AND  CLASSIFICATION 


53 


concept  into  members  which  sustain  contrary  rather  than 
contradictory  relations  to  each  other.  This  is  seen  particu- 
larly in  debate  where  an  opponent  will  often  confront  one 
with  a choice  of  alternatives,  either  this  course  or  that, 
when,  however,  there  is  a third  possibility  unnoticed,  or 
purposely  ignored.  It  is  the  third  possibility  which  we 
should  always  have  in  mind,  and  endeavor  to  discover 
whenever  the  necessities  of  a dichotomous  division  are 
forced  upon  us.  There  can  be  no  free  choice  of  the  mind 
unless  all  possibilities  are  presented. 

On  this  very  account  division  very  often  takes  a threefold 
form,  that  of  Trichotomy  ; because  when  a concept  is  divided 
into  two  members  exhibiting  some  one  or  more  opposed 
characteristics,  a third  member  representing  a mediating 
position  between  the  two  naturally  suggests  itself.  This 
form  of  division  which  expresses  extreme  terms  in  relation 
to  the  middle  ground  between  them  has  played  an  important 
role  in  the  history  of  philosophical  thought.  For  instance 
Aristotle’s  theory  of  morals  was  based  upon  the  principle 
that  right  conduct  always  lies  between  two  extremes,  neither 
of  which  commends  itself  to  the  reason.  Thus  courage,  which 
is  the  mean  between  cowardice  on  the  one  hand  and  rash- 
ness on  the  other,  takes  rank  as  a virtue  and  is  freed  from 
all  criticism  which  is  called  forth  naturally  by  the  extremes. 
So,  also,  according  to  Aristotle,  temperance  is  the  virtue 
which  avoids  the  extremes  of  ascetic  abstinence  and  un- 
bridled desire. 

The  trichotomous  division  is  further  illustrated  in  the 
dialectical  method  which  grew  out  of  the  teaching  of  Kant, 
and  which  was  developed  by  Fichte  and  brought  to  its  com- 
plete expression  by  Hegel.  The  meaning  of  “dialectic”  may 
be  gathered  from  Plato’s  usage  of  the  term,  which  with  him 
signified  the  process  of  argument  between  two  disputants, 
who  in  their  controversy  for  and  against  a given  proposition 
render  this  exceedingly  valuable  service,  namely,  that  the 
course  of  debate  brings  to  light  whatever  fundamental 


54 


DEDUCTIVE  LOGIC 


elements  of  truth  the  opposed  positions  may  have  in  com- 
mon. This  idea  Hegel  has  applied  to  the  evolution  of  all 
truth  which  he  declares  develops  progressively  through  three 
stages.  The  first  is  the  thesis,  the  primary  proposition  as 
originally  affirmed ; the  second  is  the  antithesis,  the  opposed 
proposition ; the  third  is  the  synthesis,  the  reconstruction  of 
these  two  from  a higher  point  of  view  which  discloses  the 
unity  underlying  the  two  extreme  positions.  Hegel  insists 
that  a scheme  such  as  this  forms  a universal  programme 
according  to  which  the  evolution  of  all  thought  must  pro- 
ceed. 

A distinction  is  drawn  in  logic  between  the  so-called 
empirical  and  logical  divisions.  A logical  division  is  one 
which  applies  the  principle  of  division  to  any  given  concept, 
and  notes  all  the  possible  members  of  the  division  which 
result  from  such  a process.  The  empirical  division  is  the 
result  of  a critical  examination  of  the  logical  division  to  the 
end  that  all  members  of  such  a division  which  cannot  be 
realized  actually  in  experience  may  be  eliminated.  A strictly 
logical  division  may  give  certain  ideal  groups  which  are 
rendered  impossible  actually  because  of  certain  necessities 
of  the  concrete  situation,  or  because  of  the  general  economy 
of  nature. 

As  an  illustration  of  the  former,  the  genus,  regular  poly- 
hedron, may  be  divided  according  to  the  number  of  the 
bounding  planes.  Now  applying  to  the  genus  the  principle 
of  division  which  is  the  number  series,  and  without  taking 
into  consideration  any  other  limiting  conditions  whatso- 
ever, we  get  regular  polyhedrons  according  as  their  faces 
are : — 

4, 5,  6,  7,  8,  9,  10, 11, 12, 13, 14, 15, 16, 17, 18, 19,  20,  etc. 

However,  a second  question  forces  itself  upon  our  consid- 
eration. Are  the  space  conditions  such  that  all  of  these 
supposed  regular  polyhedrons  can  be  actually  constructed? 


DIVISION  AND  CLASSIFICATION 


55 


The  answer  is  that  only  the  following  are  possible,  those 
having  sides  as  follows : — 

4,  6,  8,  12,  20. 

Thus  the  formal  division  has  been  corrected  through  an 
appeal  to  the  actual  conditions  which  are  imposed  by  the 
existent  space  relations. 

Again  to  illustrate  what  may  be  called  the  limitations  due 
to  the  economy  of  nature,  we  have  the  following  division 
of  mankind,  according  to  differences  of  color : White  men, 
black,  red,  yellow,  orange,  green,  etc. 

Such  a division  is  the  result  of  applying  a color  principle 
of  division  in  its  full  rigor  and  extent  to  the  concept  in 
question.  When,  however,  we  ask  in  addition  the  question 
as  to  the  prodigality  of  nature  in  this  respect,  we  find  that 
the  actual  colors  found  among  the  various  races  of  man  are 
limited,  and  therefore  our  division  must  be  corrected  by 
striking  out  such  colors  as  green,  orange,  etc.,  which  have 
no  empirical  confirmation  in  fact. 

There  is  a difference  as  regards  order  of  procedure  between 
dividing  a concept  simply  according  to  the  possible  varia- 
tions of  some  selected  property  irrespective  of  any  con- 
sideration of  the  actual  limitations  which  may  occur  in 
experience,  and  starting  with  actual  classes  as  they  have 
been  observed  in  experience,  and  grouping  them  together  in 
a system  as  related  members  of  one  and  the  same  genus. 
This  latter  process  is  that  of  classification  which  will  be 
considered  next. 

Classification  is  a term  which  is  used  for  the  most  part 
interchangeably  with  division,  but,  as  regards  strictly  logical 
usage,  classification  is  a process  which  is  the  inverse  of 
division  proper.  The  problem  of  classification,  therefore, 
is  that  of  arranging  given  classes  into  a system  whose 
unity  is  such  that  it  can  be  regarded  as  forming  the  under- 
lying ground  of  the  several  classes  in  question.  Moreover, 
classification  proper  represents  usually  a more  elaborate 


56 


DEDUCTIVE  LOGIC 


scheme  than  simple  division.  In  classification  the  process 
of  division  is  many  times  repeated,  so  that  the  original  genus 
not  only  has  its  species  grouped  under  it,  but  each  species  in 
turn  may  be  regarded  as  a new  genus,  and  its  corresponding 
species  indicated,  and  so  on  until  a series  of  infimaz  species  is 
reached. 

A classification  may  be  of  two  kinds,  either  artificial  or 
natural.  In  an  artificial  classification,  the  principle  of  classi- 
fication selected  is  some  characteristic  which  is  external  to 
the  essential  nature  of  the  elements  to  be  classified.  In  a 
natural  classification,  the  principle  of  classification  selected 
is  a property  which  forms  a constituent  part  of  the  essential 
nature  of  the  elements  to  be  classified. 

1.  In  an  artificial  classification  the  characteristic  which  is 
selected  as  the  basis  of  the  classification  is  either  an  accident, 
or  at  least  an  unimportant  property  of  the  elements  to  be 
classified.  The  consequence  is  that  the  various  members  of 
the  classification  which  fall  together  in  the  same  group 
possess  in  common  only  this  arbitrary  or  artificial  mark 
selected  as  the  basis  of  classification,  and  are  dissimilar  in 
all  other  respects. 

This  kind  of  a classification  is  best  illustrated  by  the 
alphabetical  catalogue  of  books  in  a library.  The  initial 
letter  of  the  author  is  regarded  as  a differentiating  mark.  It 
brings  together  in  one  group  an  indiscriminate  variety  of 
books  which  have  in  common  merely  the  one  artificial  mark. 
Such  a classification,  however,  serves  its  purpose  most  satis- 
factorily in  furnishing  a convenient  key  for  reference. 

An  artificial  classification  generally  may  be  said  to  per- 
form some  such  function  as  this,  namely,  of  realizing  some 
definite  and  specific  purpose,  and  is  therefore  essentially  a 
working  classification.  It  must  not  be  thought  that  an 
artificial  classification  is  necessarily  an  imperfect  or  unsat- 
isfactory classification.  On  the  contrary,  for  the  end  to 
which  it  is  designed,  it  serves  a most  useful  purpose. 

2.  A natural  classification  is  based  upon  one  or  more 


DIVISION  AND  CLASSIFICATION 


57 


properties  directly  connected  with  the  essential  nature  of 
the  elements  to  be  classified.  In  a natural  classification  the 
members  which  fall  together  in  the  same  group  should  not 
only  agree  as  regards  the  common  property  which  is  selected 
as  the  basis  of  the  classification,  but  also  as  regards  a large 
number  of  cognate  properties.  A property  therefore  should 
be  selected  as  the  basis  of  classification  which  has  the  largest 
number  of  correlated  properties  inseparably  connected  with 
it,  so  that  whenever  the  given  property  is  present,  the  cor- 
related properties  will  always  accompany  it.  Such  a 
property  is  known  as  a diagnostic  property.  It  is  like  the 
significant  symptom  which  indicates  to  the  physician  the 
nature  of  a disease,  because  the  symptom  in  question  always 
has  a number  of  other  symptoms  correlated  with  it  and  which 
forms  therefore  a basis  of  exact  diagnosis.  A diagnostic 
attribute,  therefore,  will  bring  together  in  one  and  the  same 
group  members  of  the  classification  which  have  in  common 
not  merely  a large  number  of  properties,  but  these  proper- 
ties form  a system  of  correlated  and  interconnected  elements 
which  together  constitute  what  is  known  as  a natural  kind. 
In  a natural  classification,  the  various  members  therefore 
form  these  groups  of  natural  kinds,  or,  as  they  are  sometimes 
called,  real  kinds.  In  a zoological  classification  we  would 
have  such  natural  kinds  as  vertebrates,  mammals,  reptiles, 
etc.  The  mammals,  for  instance,  have  not  merely  the  dif- 
ferentiating mark  in  common,  but  also  a complex  system  of 
correlated  properties  which  are  built  about  the  central  and 
distinguishing  property  of  the  kind. 

Natural  classifications  obtain  in  all  the  sciences,  wherein 
the  subject-matter  is  arranged  in  groups  according  to  a 
natural  determination  of  kind.  The  classifications  of  ani- 
mal and  plant  life  are  the  best  illustrations  which  we  have 
of  natural  classification.  A natural  classification  furnishes 
an  excellent  basis  for  comparative  study,  for,  in  the  method 
of  grouping  according  to  kind,  resemblances  are  most  easily 
observed  and  significant  relations  suggested,  while  at  the 


58 


DEDUCTIVE  LOGIC 


same  time  characteristic  differences  are  rendered  most  promi- 
nent. It  often  happens  in  a natural  classification  that  the 
fundamental  property  chosen  as  the  basis  of  the  classifica- 
tion, and  which  is  of  such  a nature  as  to  determine  the 
essential  structure  or  function  of  a definite  kind,  is  neces- 
sarily of  such  a nature  that  it  is  not  disclosed  to  a surface 
observation.  Thus  the  classification  of  birds,  for  instance, 
is  based  largely  upon  fundamental  differences  in  anatomical 
structure.  Birds,  not  as  we  see  them,  but  as  they  are  when 
stripped  of  plumage  and  in  their  nakedness,  are  the  real 
objects  of  consideration  in  such  a system  of  classification. 
The  result  is  that  in  the  same  group  there  will  appear  side 
by  side  a number  of  birds  whose  surface  markings  are 
exceedingly  disparate,  such  as  the  blue  jay  and  the  crow, 
or  the  English  sparrow  and  the  cardinal.  It  is  always  a 
broadening  experience,  as  regards  our  habits  of  thinking, 
when  we  are  able  to  discover  some  essential  similarity  at 
the  basis  of  a marked  surface  dissimilarity. 

In  arranging  the  various  cognate  species  in  any  scheme 
of  classification,  they  should  be  arranged  in  some  kind  of 
order  so  that  the  more  closely  allied  species  are  placed  side 
by  side.  It  is  not  only  necessary  to  exhibit  the  unity  under- 
lying each  distinct  species,  but  also  the  connection  which 
exists  between  several  species  closely  related  to  each  other. 
This  is  especially  to  be  desired  when  several  cognate  species 
together  form  a series  of  progressive  development.  In 
such  a series,  every  term  representing  a distinct  species 
should  occupy  a place  in  the  classification  which  will  at 
once  show  its  dependence  upon  the  terms  preceding  it, 
and  its  influence  in  turn  upon  the  terms  which  follow  it. 
Every  term  thus  looks  before  and  after,  and  the  series  as  a 
whole  is  characterized  by  an  ever  increasing  complexity  of 
attributes  and  functions.  This  principle  of  an  ordered 
series  in  classification,  which  the  doctrine  of  evolution  has 
emphasized,  is  applicable  not  merely  to  the  classification  of 
animal  and  plant  life,  but  has  a far  wider  sphere  of  applica- 


DIVISION  AND  CLASSIFICATION 


59 


tion.  Herbert  Spencer  has  taken  the  theory  of  biological 
evolution,  and  has  applied  it  with  skill  and  insight  to  the 
various  branches  of  knowledge,  as  politics,  sociology,  history, 
psychology,  ethics,  etc.,  so  that  as  a result  the  classification 
of  the  subject-matter  in  these  disciplines  shows  a graded 
series  of  progressive  development. 

The  doctrine  of  evolution,  moreover,  has  affected  the 
general  theory  of  classification  in  the  further  demand  that 
the  progressive  series  should  exhibit  as  far  as  possible  the 
transition  cases  between  the  most  closely  allied  of  cognate 
species.  In  the  traditional  view  of  classification  according  to 
natural  kinds,  it  was  held  most  stoutly  that  each  member  of  a 
series  of  cognate  species  — that  is,  each  natural  kind  — must 
be  regarded  as  cut  off  wholly  from  every  other,  even  from 
that  with  which  it  is  most  of  kin.  It  is  the  ancient  doctrine 
of  the  immutability  of  species.  The  theory  of  evolution, 
however,  insists  that  the  seemingly  distinct  species  shade 
off  by  inappreciable  degrees  of  difference,  so  that  the  gap 
between  any  two  may  be  filled  up  by  transition  cases  show- 
ing the  possibility  of  a continuous  transformation  from  one 
to  the  other.  These  transition  cases,  or  missing  links,  can- 
not always  be  supplied  in  experience ; but  the  contention  of 
the  evolutionist  is  that  in  many  cases  they  have  been 
supplied,  and  that  if  our  experience  were  not  so  limited, 
they  could  be  supplied  in  many  more.  There  is  an  illustra- 
tion, however,  which  does  show  a classification  in  which  the 
transition  cases  between  groups  may  be  shown  perfectly 
without  any  defects  due  to  the  limitations  of  experience. 
This  illustration  is  from  the  sphere  of  mathematics,  and 
therefore  is  relieved  of  the  complexities  and  consequent 
difficulties  which  obtain  in  reference  to  natural  phenomena. 
We  know  that  the  various  conic  sections  may  be  divided 
into  the  following  groups,  — the  point,  straight  line,  circle, 
ellipse,  parabola,  and  hyperbola.  These  are  not  to  be  re- 
garded as  distinct  classes,  each  one  lying  wholly  outside 
of  all  the  others,  but  as  so  related  that  the  circle  for  instance 


60 


DEDUCTIVE  LOGIC 


may  be  exhibited  as  the  special  case  of  the  ellipse,  and  that 
it  may  be  shown  how  through  a continuous  transformation 
the  ellipse  may  become  a circle.  In  like  manner,  the 
parabola  may  pass  over  into  the  ellipse  on  the  one  hand, 
or  into  the  hyperbola  on  the  other. 

When  also  limiting  cases  between  species  are  forthcoming 
in  biological  classification,  they  serve  to  form  a graduated 
series  in  which  the  presence  of  transition  cases  between 
allied  groups  discloses  their  underlying  unity.  The  tradi- 
tional doctrine  of  the  immutability  of  species  breaks  down 
in  the  face  of  such  instances.  The  distinct  groups  of  fishes 
and  amphibians  are  differentiated  by  the  presence  of  gills 
in  the  one  and  of  lungs  in  the  other.  In  the  case  of  the 
so-called  group  of  Dipnoi,  the  African  mud-fish,  there  were 
discovered  in  one  and  the  same  animal  both  lungs  and  gills. 
It  forms,  therefore,  an  intermediate  transition  type  between 
the  fishes  and  the  amphibians.  Moreover,  the  links  which 
the  existing  forms  of  animal  life  have  not  been  able  to 
supply  have  been  found  in  many  cases  in  the  record  of 
extinct  forms  preserved  in  the  various  geological  strata 
of  the  earth’s  surface. 

The  unity  of  widely  divergent  species  is  illustrated  by 
Yon  Baer’s  law,  that  the  history  of  evolution  of  species  in 
the  race  is  repeated  in  miniature  in  the  development 
observed  in  the  embryo  of  each  individual.  Thus  the  egg 
of  a bird  in  the  various  stages  of  transformation  passes 
through  a series  of  forms,  resembling  in  a rough  way  it  is 
true,  but  still  resembling  successively  a worm,  then  a fish, 
then  an  amphibian,  then  a reptile,  and  finally  the  full- 
formed  bird.  That  all  these  variations  in  form  are  due  to 
variations  in  the  one  constructive  basal  principle  is  clearly 
seen,  inasmuch  as  the  different  transformations  occur  within 
the  one  organism,  bounded  by  the  enveloping  wall  of  the 
egg.  It  is  the  function  of  classification,  therefore,  to  show 
whenever  it  is  possible  the  unity  which  underlies  its  various 
groups,  and  holds  them  together  in  a single  system  through 


DIVISION  AND  CLASSIFICATION 


61 


bonds  not  of  external  relation  merely,  but  of  an  inner  kin- 
ship. 

Every  science  naturally  seeks  to  arrange  its  material  in 
an  orderly  manner  which  results  in  some  scheme  of  classifi- 
cation. In  the  sciences  such  as  zoology  and  botany,  the 
systems  of  classification  are  developed  to  such  an  extent  of 
detail  that  the  intermediate  genera  and  species  between  the 
summum  genus  and  the  infima  species  are  specified  by  a 
series  of  terms  which  serve  to  indicate  a more  and  more 
elaborate  degree  of  specification.  These  terms  in  their 
order  of  specification  are  as  follows : kingdom,  group,  sphere, 
class,  order,  family,  tribe,  genus,  subdivision,  species,  variety, 
and  finally,  the  separate  individuals.  These  terms  may  not 
all  be  used  in  any  one  system,  but  they  form  a kind  of 
skeleton  scheme,  any  parts  of  which  are  available  for  the 
general  purposes  of  classification.  It  should  be  remembered 
in  this  connection  that  the  terms  genus  and  species,  accord- 
ing to  logical  usage,  are  to  be  regarded  always  as  relative 
terms  applicable  to  any  classes  whatever,  which  are  sub- 
ordinated one  to  the  other.  Thus  the  term  order  is  a genus 
as  regards  the  family,  but  species  as  regards  the  class. 

In  a system  of  classification,  the  names  assigned  to 
various  species  are  often  compound  terms  made  up  of  the 
genus  and  differentia  of  the  species,  e.g.  fringed  gentian, 
red-winged  blackbird,  smooth-coated  collie,  etc.  The  name 
not  only  indicates  its  place  in  the  general  system  of  classifi- 
cation, but  is  at  the  same  time  a shorthand  expression  of  its 
definition. 

Not  only  has  each  science  a classification  of  its  own 
material,  but  attempts  have  been  made  also  from  time  to 
time  to  classify  the  various  sciences  in  some  one  general 
system  which  shall  show  their  essential  relations  and 
dependencies.  This  has  proved  to  be  a most  engaging 
problem  to  philosophical  minds,  a problem,  however,  as 
perplexing  as  it  is  absorbing.  There  have  been  three 
attempts  in  modern  times  which  are  of  special  interest,  — 


62 


DEDUCTIVE  LOGIC 


the  classification  of  the  general  branches  of  knowledge  by 
Bacon,  and  the  classifications  of  the  sciences  by  Comte  and 
Spencer. 

Bacon’s  classification  of  all  learning,  his  so-called  “ Intel- 
lectual Globe,”  is  based  upon  the  threefold  division  of  the 
mind,  — memory,  imagination,  and  reason,  to  which  corre- 
spond the  three  general  divisions  of  learning,  history,  poetry, 
and  philosophy.  The  classification  in  its  main  lines  and 
without  going  into  all  its  minute  ramifications  is  shown  on 
facing  page.1 

This  classification  affords  abundant  scope  for  the  exercise 
of  one’s  critical  faculty  as  regards  the  validity  of  the  various 
divisions  which  Bacon  makes  in  the  course  of  his  analysis 
of  human  learning. 

Bacon  insisted  that  every  classification  of  human  knowl- 
edge should  exhibit  its  various  members  as  branches  con- 
nected with  a common  trunk  ; the  classification  of  Comte  is 
based  upon  a principle  radically  different.  His  purpose  is 
to  show  the  various  sciences  in  their  order  of  progressive 
development.  He  insists  that  together  they  form  a series 
of  increasing  complexity  in  which  each  science  is  dependent 
upon  those  before  it,  and  is  itself  a natural  propsedeutic  to 
those  which  follow  it. 

Comte’s  classification  of  the  sciences  proceeds  in  the  follow- 
ing order : Mathematics,  Astronomy,  Physics,  Chemistry, 
Biology,  Sociology,  the  Science  of  Morals.  In  order  that 
the  significance  of  this  series  may  be  fully  appreciated,  the 
following  passage  from  Comte  is  appended  : — 

“ In  morals  we  study  human  nature  for  the  government 
of  human  life.  All  our  real  speculations,  the  most  abstract 
and  the  most  simple  not  excepted,  necessarily  converge  toward 
this  human  domain,  for  indirectly  they  help  us  to  the  knowl- 
edge of  man  under  his  lower  aspects,  on  which  the  nobler  are 
dependent.  . . . Paramount  as  the  theory  of  our  emotional 
nature,  studied  in  itself,  must  ultimately  be,  without  this 
1 Bacon,  The  Dignity  and  Advancement  of  Learning,  Book  II,  etc. 


Human  Learning- 


DIVISION  AND  CLASSIFICATION 


63 


G4 


DEDUCTIVE  LOGIC 


preliminary  step  it  would  have  no  consistence.  Morals  thus 
objectively  made  dependent  on  Sociology,  the  next  step  is 
easy  and  similiar;  objectively  Sociology  becomes  dependent 
on  Biology,  as  our  cerebral  existence  evidently  rests  on  our 
purely  bodily  life.  These  two  steps  carry  us  on  to  the  con- 
ception of  Chemistry  as  the  normal  basis  of  Biology,  since 
we  allow  that  vitality  depends  on  the  general  law  of  the 
combination  of  water.  Chemistry  again  in  its  turn  is  ob- 
jectively subordinate  to  Physics,  by  virtue  of  the  influence 
which  the  universal  properties  of  matter  must  always  exer- 
cise on  the  specific  qualities  of  the  different  substances. 
Similarly  Physics  become  subordinate  to  Astronomy  when 
we  recognize  the  fact  that  the  existence  of  our  terrestrial 
environment  is  carried  on  in  perpetual  subjection  to  the  condi- 
tions of  our  planet  as  one  of  the  heavenly  bodies.  Lastly, 
Astronomy  is  subordinated  to  Mathematics  by  virtue  of 
the  evident  dependence  of  the  geometrical  and  mechanical 
phenomena  of  the  heavens  on  the  universal  laws  of  number, 
extension,  and  motion.” 1 

Mr.  Spencer  takes  exception  to  Comte’s  arrangement  of 
the  sciences  in  serial  order,  insisting  that  such  a grouping 
of  the  sciences  represents  neither  their  logical  dependence 
or  their  historical  dependence.  In  this  connection  he  gives 
his  definition  of  a true  classification  which  may  be  of  inter- 
est to  quote  here  as  we  have  already  emphasized  the 
fundamental  principle  which  lies  at  its  basis.  “ A true  classi- 
fication,” says  Mr.  Spencer,  “ includes  in  each  class  those 
objects  which  have  more  characteristics  in  common  with  one 
another,  than  any  of  them  have  in  common  with  any  objects 
excluded  from  the  class.  Further,  the  characteristics  pos- 
sessed in  common  by  the  colligated  objects,  and  not  possessed 
by  other  objects,  involve  more  numerous  dependent  charac- 
teristics. There  are  two  sides  of  the  same  definition.  For 
things  possessing  the  greatest  number  of  attributes  in  com- 
mon are  things  that  possess  in  common  those  essential  at- 

1 Comte,  System  of  Positive  Polity,  Vol.  IV,  pp.  161-162. 


DIVISION  AND  CLASSIFICATION 


65 


tributes  on  which  the  rest  depend;  and,  conversely,  the 
possession  in  common  of  the  essential  attributes  implies  the 
possession  in  common  of  the  greatest  number  of  attributes.”1 
The  classification  of  Mr.  Spencer  proceeds  upon  this 
principle  with  the  following  result:  — 


that  which  treats  of 
the  forms  in  which 
phenomena  are 
known  to  us 


Abstract  Science 


Logic 

Mathematics 


Science  is 


or 


that  which  treats 
of  the  phenom- 
ena themselves 


in  their  f ^tract- 

elements  concrete 
[ Science 


in  their  f Concrete 
totalities  | Science 


Mechanics 

Physics 

Chemistry 

etc. 

Astronomy 

Geology 

Biology 

Psychology 

Sociology 

etc.2 


In  the  above  the  terms  abstract,  abstract-concrete,  con- 
crete, need  some  further  explanation  in  order  that  one  may 
understand  the  sense  in  which  Mr.  Spencer  uses  them.  By 
abstract  sciences  he  would  designate  those  sciences  which 
deal  with  fundamental  principles  detached  from  any  par- 
ticular incidents  which  may  illustrate  them  ; as,  for  in- 
stance, the  necessary  relations  which  obtain  in  logic  and 
mathematics  and  which  maybe  proved  and  formulated  quite 
apart  from  any  concrete  demonstration.  By  the  compound 
term  abstract-concrete  he  means  those  sciences  which  are 
partly  concrete  inasmuch  as  they  investigate  actual  phenom- 
ena themselves,  but  abstract  inasmuch  as  the  phenomena 
investigated  are  only  detached  portions  of  more  complete 

1 Spencer,  Essays,  Scientific,  Political,  and  Speculative,  Vol.  II,  p.  76. 

2 Ibid.,  Vol.  II,  p.  78. 


6G 


DEDUCTIVE  LOGIC 


wholes,  as,  for  instance,  the  examination  in  chemistry  of  the 
special  properties  of  oxygen  by  themselves  and  apart  from 
the  whole  body  of  chemical  phenomena.  By  the  purely  con- 
crete sciences,  Mr.  Spencer  refers  to  those  sciences  which 
investigate  phenomena  pertaining  to  complete  aggregates, 
and  the  relation  of  all  separate  parts  to  one  combined 
whole.  Thus,  as  Mr.  Spencer  says  : “ The  geologist  does  not 
take  for  his  problem  only  those  irregularities  of  the  earth’s 
crust  that  are  worked  by  denudation  ; or  only  those  which 
igneous  action  causes.  He  does  not  seek  simply  to  under- 
stand how  sedimentary  strata  were  formed;  or  how  faults 
were  produced ; or  how  moraines  originated ; or  how  the 
beds  of  Alpine  lakes  were  scooped  out.  But  taking  into 
account  all  agencies  cooperating  in  endless  and  ever  varying 
combinations,  he  aims  to  interpret  the  entire  structure  of 
the  earth’s  crust.  If  he  studies  separately  the  actions  of 
rain,  rivers,  glaciers,  icebergs,  tides,  waves,  volcanoes,  earth- 
quakes, etc.,  he  does  so  that  he  may  be  better  able  to 
comprehend  their  joint  actions  as  factors  in  geological 
phenomena,  the  object  of  his  science  being  to  generalize 
these  phenomena  in  all  their  intricate  connexions  as  parts 
of  one  whole.”1 

These  classifications  of  Bacon,  Comte,  and  Spencer  have 
been  given  here  somewhat  at  length  inasmuch  as  they  pre- 
sent an  excellent  idea  of  the  difficulties  attending  the  classi- 
fication of  such  complex  phenomena,  as  well  as  to  furnish 
suitable  material  for  the  exercise  of  one’s  critical  faculty  in 
respect  to  the  measure  in  which  these  systems  have  realized 
the  rigorous  requirements  of  the  laws  of  classification. 

1 Spencer,  Essays,  Scientific,  Political,  and,  Speculative,  Vol.  II,  p.  89. 


CHAPTER  VII 


THE  SINGULAR  JUDGMENT 

This  type  of  judgment  differs  from  the  universal  judg- 
ment in  the  essential  feature  that  it  refers  a single  object  of 
thought  to  our  general  body  of  knowledge  which  serves  to 
interpret  it,  while  the  universal  judgment  is  concerned  solely 
with  the  universal  characteristics  and  relations  which  obtain 
within  the  general  body  of  knowledge  itself.  The  singular 
judgment  deals  with  special  eases  in  the  light  of  our  gen- 
eral knowledge.  The  universal  judgment  deals  only  with 
the  various  phases  of  general  knowledge  in  the  light  which 
is  reflected  from  one  part  to  another.  The  single  instance 
which  forms  the  subject  of  the  singular  judgment  may  be 
actually  present  in  the  field  of  perception,  or  it  may  be  re- 
instated in  consciousness  through  the  processes  of  memory. 
The  change  in  tense  may  be  regarded  as  unessential,  and 
the  term  perceptive  judgment  is  often  used  as  synonymous 
with  singular  judgment,  whether  the  given  perception  is  in 
the  past  or  present  time.  The  so-called  narrative  judgment 
is  only  the  perceptive  judgment  referred  to  past  time,  and 
therefore  does  not  constitute  a distinct  type  of  judgment. 

If  the  whole  field  of  perception  is  taken  in  an  indefinite 
manner  as  the  object  of  thought,  and  no  particular  part 
of  it  specified  for  special  consideration,  then  the  judgment 
which  results  is  known  as  the  impersonal  judgment,  e.g.  It 
is  raining,  it  is  hot,  it  is  a charming  day,  etc.  The  imper- 
sonal pronoun  in  such  judgments  refers  to  reality  which  is 
present  in  consciousness  in  a wholly  undifferentiated  man- 
ner. If,  however,  this  indefinite  range  of  reality  is  more 
precisely  determined  by  focussing  the  consciousness  at  any 

67 


68 


DEDUCTIVE  LOGIC 


one  particular  point  in  the  field  of  perception,  we  have  as  a 
result  the  so-called  demonstrative  judgments,  introduced  by 
the  demonstrative  pronoun  or  adjective,  e.g.  This  is  magnetic 
ore ; this  black  sand  is  magnetic  ore.  The  latter  is  really  a 
combination  of  two  judgments,  This  is  black  sand,  and  it 
is  magnetic.  The  perceptive  judgment  always  originates  at 
the  focal  point  of  the  perceptual  processes,  just  as  the  uni- 
versal judgment  originates  at  the  focal  point  of  the  concep- 
tual processes.  A similar  variety  of  assertion  is  also  possible 
in  reference  to  the  perceptive  or  singular  judgment  as  was 
found  to  obtain  in  reference  to  the  universal  judgment. 
Thus  the  single  subject  in  perception,  or  in  memory,  may 
be  rendered  definite  by  referring  it  to  its  appropriate  genus 
or  species,  or  by  describing  it  by  its  properties,  differentia,  or 
accidents. 

There  are  two  functions  of  the  perceptive  judgment  which 
correspond  in  a general  way  to  the  two  functions  of  definition 
and  division.  Corresponding  to  definition  there  is  the  func- 
tion of  determinate  reference.  And  corresponding  to  division 
there  is  the  function  of  indeterminate  reference. 

1.  By  determinate  reference  is  meant  the  identification 
of  the  single  object  of  perception  in  question  with  its  ap- 
propriate genus  or  species,  e.g.  That  is  a fossil  of  the  car- 
boniferous age.  In  such  a judgment  we  have  satisfactorily 
disposed  of  the  single  object  of  perception  by  referring  it  to 
the  general  class  to  which  it  belongs.  It  is  a process  simi- 
lar to  that  of  definition.  Indeed,  this  judgment  may  lead 
naturally  to  a definition  of  the  general  class  to  which  we  refer 
the  specific  object  before  us;  for  the  question  may  be  put, 
What  is  a fossil  of  the  carboniferous  age  ? The  answer 
would  be  its  definition.  In  every  process  of  referring  a 
single  object  of  perception  to  the  concept  which  explains  it, 
the  knowledge  of  the  definition  of  the  concept  employed  is 
always  implicit  in  such  a judgment.  It  is  not  explicitly 
stated,  however,  unless  the  terms  used  need  to  be  further 
explained  or  illustrated.  It  should  be  remembered  that  a 


CHAPTER  VIII 


THE  NEGATIVE  JUDGMENT 

So  far  in  this  discussion,  judgments  of  assertion  only,  or 
affirmative  judgments,  have  been  under  consideration.  We 
come  now  to  the  examination  of  the  negative  judgment. 
We  have  seen  that  the  function  of  the  copula  in  the  affirma- 
tive judgment  is  to  fuse  into  one  the  subject  and  predicate 
terms  of  the  universal  judgment,  and  in  the  singular  judg- 
ment to  assert  that  the  given  object  in  the  field  of  percep- 
tion or  in  memory  is  one  with  the  concept  to  which  it  is 
referred.  The  process  in  either  case  is  essentially  con- 
structive. 

The  negative  judgment,  on  the  other  hand,  holds  apart  the 
subject  and  predicate  terms.  It  denies  the  possibility  of 
explaining  the  one  concept  by  the  other,  or  of  interpreting 
the  single  case  by  the  universal  in  question.  The  negative 
judgment  stands  guard  over  our  general  body  of  knowledge, 
excluding  whatever  is  altogether  false,  and  also  whatever 
may  be  false  under  certain  conditions  but  may  be  true 
under  others.  It  is  thus  through  the  process  of  the  nega- 
tive judgment  that  thought  becomes  discriminating.  Our 
first  judgments  upon  any  unfamiliar  subject  are  most 
naturally  vague  and  indefinite.  The  truth  which  they 
contain  is  mingled  with  much  that  is  erroneous.  It  may  be, 
as  is  often  the  case,  that  a given  object  of  perception  is 
recognized  as  belonging  to  a certain  genus,  but  we  do  not 
know  to  which  one  of  several  species  under  this  genus  it 
should  be  assigned.  But  as  our  knowledge  grows,  the 
various  special  cases  become  distinct  through  well-recognized 
differences,  which,  when  stated,  constitute  a series  of  negative 

73 


74 


DEDUCTIVE  LOGIC 


judgments.  This  process  of  differentiation  serves  to  render 
knowledge  more  exact.  This  is  essentially  the  method 
which  Socrates  pursued  with  his  pupils,  asking  of  them  the 
meaning  of  some  idea,  such  as  virtue,  or  justice,  and  then 
examining  the  conventional  definition  given  in  the  light  of 
certain  concrete  instances  of  virtue  or  of  justice  which 
differed  radically  from  the  definition.  Accordingly  the 
definition  had  to  be  changed  so  as  to  adapt  itself  to  these 
negative  cases.  In  this  manner  vague  and  general  notions 
upon  which  little  thought  had  been  bestowed  were  trans- 
formed into  clear  and  precise  ideas.  The  old  dictum,  Omnis 
determinatio  est  negatio,  expresses  the  essential  function  of 
the  negative  judgment  as  that  of  exact  determination  through 
the  process  of  negation.  This  process  of  negation  sets  a 
limit  beyond  which  a given  concept  cannot  be  applied.  A 
limit  thus  set  serves  as  a boundary  of  exact  determination. 
It  marks  always  a line  of  distinction  between  what  is  and 
what  is  not  as  regards  the  essential  nature  of  any  concept. 
The  process  of  exact  determination  by  means  of  negation 
may  be  analyzed  into  its  three  component  stages  which  form 
the  programme  of  all  exact  thinking  : — 

1.  The  first  rough  draft  of  knowledge,  which  is  neces- 
sarily vague  and  indefinite. 

2.  The  critical  limitation  of  this  primary  assertion  by  a 
number  of  negative  judgments,  which  show  where  it  breaks 
down,  where  it  does  not  apply,  and  wherein  the  unessential 
may  be  eliminated. 

3.  The  reconstruction  of  the  original  statement  modified 
by  the  necessary  restrictions,  which  the  process  of  negative 
criticism  has  disclosed  as  essential.  The  result  is  knowdedge 
in  exact  and  definite  form. 

Thus  the  beginner  in  the  study  of  chemistry  has  a vague 
idea  of  chemical  affinity,  — that  certain  elements  enter  into 
a number  of  various  combinations  to  form  compounds.  But 
as  his  knowledge  grows,  he  finds  himself  face  to  face  with  a 
series  of  negative  facts,  which  must  be  reckoned  with, — ■ 


THE  NEGATIVE  JUDGMENT 


75 


namely,  that  all  elements  indiscriminately  do  not  combine 
together ; that  they  which  are  capable  of  combining  do  not  do 
so  in  any  proportions  whatsoever ; that  combinations  which 
are  possible  under  certain  temperature  conditions  are  not  in 
others ; that  elements  which  unite  under  ordinary  circum- 
stances will  not  unite  in  the  presence  of  certain  other 
elements.  Consequently,  when  the  idea  of  chemical  affinity 
comes  to  be  restated  in  the  thought  of  the  advanced  student 
of  the  subject,  it  must  be  necessarily  more  definite  and  exact 
by  reason  of  these  very  negative  instances  which  have 
emerged  in  the  course  of  his  investigations. 

Moreover,  every  negative  judgment  which  possesses  any 
value  as  knowledge  must  rest  upon  some  positive  ground. 
Mere  denial  of  itself  means  nothing.  For  when  pushed  for 
a reason  of  our  denial,  we  must  be  prepared  to  give  some 
positive  ground  for  the  conviction  that  is  in  us.  When  we 
say,  It  will  not  rain  to-night,  our  judgment  rests  upon  our 
interpretation  of  the  actual  weather  conditions.  We  venture 
the  negative  statement  because  we  are  positive  concerning 
the  significance  of  the  present  atmospheric  conditions.  And 
also,  if  we  should  say  of  a certain  friend,  He  did  not  do 
the  mean  act  of  which  he  is  accused,  we  rest  such  a denial 
upon  our  knowledge  of  his  character,  abundantly  tested  and 
proved  by  years  of  close  companionship.  If  a person  should 
affirm  that  he  does  not  expect  to  be  conditioned  in  a certain 
examination,  and  the  only  ground  he  could  allege  for  his 
belief  were  merely  the  indefinite  feeling  that  he  would 
not  fail,  such  an  uncertain  foundation  would  be  absolutely 
worthless.  A definite  negation  must  have  the  ground  of 
definite  knowledge,  or  otherwise  it  has  no  force. 

A distinction  moreover  is  often  drawn  between  signifi- 
cant and  non-significant  denial.  Significant  denial  occurs 
within  the  region  which  lies  near  the  line  of  differentiation 
between  affirmation  and  negation.  The  non-significant  de- 
nial occurs  in  the  region  remotely  separated  from  this  line 
of  differentiation.  Thus,  to  say  that  a chrysanthemum  is 


76 


DEDUCTIVE  LOGIC 


not  an  animal  would  be  a non-significant  denial.  But  to 
say  that  one  of  the  lower  orders  of  animal  such  as  that  of 
the  sea-anemone  is  not  a chrysanthemum  would  be  a sig- 
nificant denial,  because  it  resembles  the  chrysanthemum  in 
external  appearance.  There  are  so  many  marks  in  common 
that  one  may  fail  to  recognize  at  the  first  glance  the 
differentiating  mark  which  separates  the  two  cases. 

Significant  denial  often  carries  with  it  also  the  implication 
that  under  certain  changed  conditions  the  relation  or  refer- 
ence which  is  denied  would  become  true.  Thus  the  state- 
ment that  water  does  not  boil  on  the  top  of  a mountain  at 
212°,  implies  that  it  would  boil  however  at  some  other  tem- 
perature. If  we  say  that  the  elements,  oxygen  and  hydrogen, 
will  not  unite  in  a one-to-one  proportion,  there  is  the  impli- 
cation that  they  will  unite  in  some  other  proportion.  Again 
the  statement,  that  a certain  man  having  made  such  a politi- 
cal blunder  could  not  be  nominated  for  governor,  implies 
that  had  it  not  been  for  the  political  blunder  in  question,  he 
might  have  been  nominated  for  governor.  A distinction 
however  should  be  drawn  between  limiting  conditions  and 
conditions  whose  removal  do  not  alter  the  force  of  the 
original  denial.  Thus  in  the  statement,  Do  not  trust  the 
Greeks  bearing  gifts,  the  phrase  “bearing  gifts”  is  not  a 
limiting  condition,  the  removal  of  which  would  alter  the 
statement  at  all.  The  meaning  is,  Do  not  trust  the  Greeks 
even  though  they  bear  gifts  ; that  is,  do  not  trust  them  at 
all.  Likewise  the  statement,  There  are  no  ghosts  in  mod- 
ern times,  should  not  be  interpreted  as  meaning  that  there 
were  ghosts  in  ancient  times.  The  nearer  incompatible  con- 
cepts approach  a limit  beyond  which  denial  passes  over  into 
assertion  the  more  significant  does  the  denial  become,  and 
the  greater  the  possible  difference  of  opinion  which  may 
arise  in  reference  to  it.  It  is  in  the  field  immediately  adja- 
cent to  the  limiting  cases  that  dispute  arises.  When  I say 
that  the  American  Beauty  rose  is  not  yellow,  no  one  disputes 
such  an  assertion ; and,  moreover,  there  is  no  suggestion  in 


THE  NEGATIVE  JUDGMENT 


77 


this  statement  as  to  the  real  color  of  the  American  Beauty. 
But  if  I say  that  a certain  shade  of  red  does  not  match  a 
given  sample,  the  denial  on  my  part  may  provoke  a differ- 
ence of  opinion ; and  because  the  range  of  variation  is  so 
narrow,  the  implication  is  that  the  true  color  must  be  very 
near  the  one  mentioned  and  within  the  region  of  the  various 
shades  of  red. 

If  denial  asserts  an  incompatibility  between  concepts 
which  is  absolute,  — that  is,  if  there  is  no  common  point  of 
similarity  at  all  between  them,  — the  judgment  is  called  an 
infinite  negation.  Such  judgments  being  completely  with- 
out significance  are  always  nonsensical ; e.g.  A stone  has  no 
conscience.  A triangle  has  no  lungs.  Between  the  limit  on 
the  one  hand  of  the  infinite  negation,  and  on  the  other  of 
the  limiting  case  which  separates  denial  from  assertion, 
there  are  all  grades  of  denial  possible  according  to  the  order 
of  their  growing  significance.  Near  the  limit  of  assertion 
denial  becomes  the  subject  of  dispute  and  controversy. 
Further  removed  the  denial  is  unquestioned.  Further  still, 
it  becomes  a truism,  a commonplace  of  knowledge,  soon 
passing  into  the  region  of  the  grotesquely  absurd  and  mean- 
ingless. To  know  just  where  assertion  ends  and  where 
denial  begins  is  characteristic  of  the  exact  mind ; to  know 
just  where  denial  ceases  to  be  significant  is  characteristic  of 
the  relevant  mind. 


CHAPTER  IX 


THE  CATEGORICAL,  HYPOTHETICAL,  AND  DISJUNCTIVE 
JUDGMENTS 

There  are  three  forms  which  our  judgments  may  take, — 
the  categorical,  hypothetical,  and  disjunctive. 

The  categorical  judgment  is  assertion  in  its  simplest  form, 
unconditioned,  unanalyzed,  and  unexplained ; e.g.  That  man 
is  a half-breed ; whales  are  mammals.  It  expresses  either 
a fact,  or  else  a generalization  based  upon  a number  of 
facts. 

The  hypothetical  judgment  is  an  assertion  subject  to  a 
given  limitation,  or  regarded  under  certain  specified  condi- 
tions. It  does  not  refer  to  a concrete  special  case,  but 
rather  to  the  abstract  universal  relations  which  form  the 
ground  of  all  the  possible  special  cases  which  may  be  con- 
ditioned by  the  relations ; e.g.  If  in  an  isosceles  triangle  a 
line  is  drawn  from  the  apex  perpendicular  to  the  base,  it 
will  bisect  it;  if  hydrogen,  oxygen,  and  sulphur  unite  in 
the  proportions  H^S04,  they  will  form  sulphuric  acid. 

Our  knowledge,  it  must  be  remembered,  forms  a system 
of  interrelated  parts.  The  hypothetical  judgment  is  con- 
cerned essentially  with  the  necessary  connections  which 
obtain  between  these  various  elements.  It  asserts  the 
fundamental  relations  which  exist  between  any  ground  and 
its  consequence.  In  our  body  of  knowledge  regarded  as  a 
system,  the  hypothetical  judgments  constitute  the  basal 
lines  of  construction ; by  them  part  is  related  to  part,  and 
part  to  the  whole. 

The  disjunctive  judgment  is  an  indeterminate  assertion 
concerning  various  possibilities  which  may  exist  in  refer- 

78 


VARIETIES  OF  JUDGMENT  FORMS  79 

ence  to  a given  subject,  and  which  are  of  such  a nature  that 
the  establishment  of  the  truth  of  any  one  necessarily  excludes 
the  others ; e.g.  The  invading  fleet  may  attack  Newport,  Cape 
Cod,  or  Gloucester.  One  may  travel  from  New  York  to 
Philadelphia  by  the  Reading,  or  the  Pennsylvania  rail- 
roads. 

We  have  divided  all  judgments  into  two  general  types, 
— the  singular  judgment  and  the  universal.  Of  these,  the 
singular  judgment  is  naturally  categorical,  for  it  is  an 
assertion  concerning  a fact  or  a group  of  facts.  If  the 
categorical  is  changed  in  form  so  as  to  make  it  a hypo- 
thetical, this  is  done  by  reason  of  a universal  hypothetical 
judgment  of  which  the  singular  hypothetical  judgment  in 
question  is  merely  a special  case,  and  therefore  the  hypo- 
thetical nature  is  due  to  the  universal  relation  which  is  as- 
sumed as  underlying  it.  Thus  in  the  judgment,  If  this 
substance  is  an  acid,  it  will  turn  blue  litmus  paper  red,  we 
see  that  the  hypothetical  relation  expressed  concerning  the 
special  case  is  merely  a single  instance  of  a relation  which 
holds  universally.  It  is  only  in  this  indirect  manner  that 
a hypothetical  judgment  can  apply  to  a special  case.  The 
hypothetical  is  essentially  a mode  of  expressing  universal 
relations.  There  are  two  cases  in  which  the  hypothetical 
form  of  judgment  is  naturally  used. 

1 . When  we  wish  to  express  the  necessary  connection  of 
cause  and  effect  between  any  given  elements  in  a system 
of  related  parts,  e.g.  If  you  double  the  pressure,  you  halve 
the  volume  of  gases. 

2.  When  we  wish  to  express  a more  exact  differentiation 
of  our  concepts  by  means  of  a reference  to  their  specific 
differences,  e.g.  If  a triangle  has  two  of  its  sides  equal,  it 
is  an  isosceles  triangle.  The  hypothetical  form  is  used  also 
when  the  differentiating  mark  cannot  be  regarded  as  of  the 
essence  of  the  concept  in  question,  and  even  when  it  is  abso- 
lutely arbitrary,  provided  only  it  serves  to  point  out  unmis- 
takably the  concept  in  question.  Thus  the  signal  of  Paul 


80 


DEDUCTIVE  LOGIC 


Revere  was  in  this  form,  If  the  enemy  come  by  land,  there 
will  be  a single  light  in  the  belfry  ; if  by  sea,  two  lights. 

The  essential  function  of  the  hypothetical  is  to  show  this 
relation  of  dependence  of  any  one  element  upon  another  in  a 
system  of  interrelated  and  coordinated  parts.  The  system  it- 
self may  be  one  of  nature,  or  one  arbitrarily  assumed  or  agreed 
upon  by  mutual  consent,  or  of  common  convention.  The 
main  thing  is  that  the  system  should  be  of  such  a nature 
as  to  render  the  connection  which  constitutes  the  hypotheti- 
cal relation  absolutely  uniform  and  necessary. 

It  is  of  course  possible  to  change  any  categorical  judg- 
ment of  the  universal  form  into  a hypothetical.  Thus, 
All  crows  are  black,  may  be  put  into  the  form,  If  there  is  a 
crow,  it  is  black.  The  hypothetical  in  this  case  is  however 
not  the  natural  form  of  expression,  and  the  reason  is  that 
in  such  a judgment  the  necessary  connection  of  ground  and 
consequent  is  not  brought  to  the  fore.  There  must  be 
in  the  very  constitution  of  the  crow  a sufficient  ground 
for  its  customary  color ; nevertheless  its  precise  nature  is 
unknown  and  lies  in  the  background  of  the  simple  asser- 
tion itself.  It  can  be  said  therefore  in  general  that  when 
a universal  judgment  presents  an  unanalyzed  content,  it 
takes  the  categorical  form  ; when  however  the  content  is 
analyzed  so  as  to  exhibit  within  it  the  connection  of  ground 
and  consequent,  then  it  takes  the  hypothetical  form. 

Again,  the  disjunctive  judgment  naturally  expresses  a 
universal  relation.  When  it  refers,  as  it  often  does,  to  a 
special  case,  the  disjunction  is  really  based  upon  our  knowl- 
edge of  general  conditions.  When  we  say,  for  instance, 
that  a certain  line  must  be  equal  to,  greater  than,  or  less 
than  some  other  given  line,  we  do  so  because  we  know  that 
any  line  whatsoever  must  be  equal  to,  greater  than,  or  less 
than  any  other  given  line.  So  also  a physician  may  pronounce 
a suspicious  case  of  sore  throat  to  be  either  scarlet  fever  or 
diphtheria.  His  judgment  in  this  case  is  grounded  wholly 
upon  his  knowledge  of  such  cases  in  general.  Therefore, 


VARIETIES  OF  JUDGMENT  FORMS 


81 


although  the  disjunctive  judgment  may  in  form  deal  with 
a single  instance,  it  always  contains  by  implication  a refer- 
ence to  the  universal  conditions  which  are  illustrated  in  the 
special  case. 

The  disjunctive  judgment,  moreover,  contains  both  a 
categorical  and  a hypothetical  element.  It  is  categorical 
inasmuch  as  it  asserts  a definite  area  of  possibility.  It  is 
hypothetical  inasmuch  as  the  possibilities  are  related  in 
such  a manner  that  if  any  one  is  true,  the  others  are  false, 
and  if  any  one  is  false,  one  of  the  others  must  be  true. 
Such  a hypothetical  implication  renders  the  disjunctive 
judgment  significant;  otherwise  it  would  be  without  mean- 
ing. To  illustrate  this,  let  us  examine  the  following  dis- 
junctive judgment,  A certain  murder  was  committed  by  an 
enemy  or  by  a burglar.  The  categorical  element  in  this 
assertion  limits  the  possibilities  to  the  two  alternatives 
mentioned,  and  excludes  suicide  or  any  other  possibility. 
The  hypothetical  element  lies  in  the  implication  that  if 
either  one  of  the  possibilities  is  proved,  it  negatives  the 
other. 

Moreover,  the  categorical,  disjunctive,  and  hypothetical 
judgments  may  be  regarded  as  various  stages  in  the  prog- 
ress of  knowledge  from  that  which  is  indefinite  and  inde- 
terminate to  that  which  is  definite  and  determinate. 

The  categorical  judgment  represents  the  primary  stage 
of  vague  assertion,  wherein  the  conditions  upon  which  the 
asserted  fact  depends  have  not  been  fully  analyzed. 

The  disjunctive  is  a statement  of  the  various  antecedents 
which  may  have  given  rise  to  the  given  fact. 

The  hypothetical  is  the  critical  analysis  of  these  various 
antecedents,  and  the  determination  of  that  particular  one 
which  bears  an  essential  and  necessary  relation  to  the  fact 
in  question. 

All  knowledge  necessarily  begins  with  a vague  assertion. 
The  very  fact  that  it  is  a beginning  renders  the  assertion 
vague.  We  hear,  for  instance,  that  a man  has  died  suddenly 


82 


DEDUCTIVE  LOGIC 


under  suspicious  circumstances.  Our  first  statement  is 
merely  that  a murder  has  been  committed.  A closer  exam- 
ination of  the  surroundings  will  suggest  various  possibilities 
by  way  of  explanation.  We  settle  finally  upon  the  definite 
conviction  that  the  murder  was  committed  by  an  enemy; 
because  we  know  that  the  dead  man  had  an  enemy  who 
had  repeatedly  threatened  to  take  his  life,  and  we  have 
therefore  the  general  hypothetical  principle  to  guide  us, 
that  if  a man  has  an  enemy  who  has  repeatedly  threatened 
to  take  his  life,  that  man’s  murder  may  be  presumably 
traced  to  this  as  its  explanation,  provided  there  are  no 
other  guiding  indications.  Or  if  the  question  should  be 
raised  as  to  which  one  of  several  possible  species  is  referred 
to  in  any  given  instance,  then  we  have  a series  of  significant 
hypothetical  to  assist  us  in  the  exact  determination.  We 
may  have  the  disjunctive  statement  that  whales  are  either 
sperm  whales  or  right  whales.  This  is  more  precisely  de- 
termined in  our  body  of  general  knowledge  by  means  of 
the  two  hypotheticals : if  the  whale  does  not  have  in  its 
mouth  baleen  or  whalebone,  it  is  a sperm  whale ; but  if  it 
has  baleen  in  its  mouth,  it  is  a right  whale. 

The  process  of  the  exact  determination  of  a disjunctive 
judgment  may  be  effected  through  a series  of  negative  judg- 
ments as  well  as  positive.  Instead  of  determining  any  one 
member  of  a disjunction  positively,  by  discovering  its  differ- 
entia or  necessary  condition,  we  may  reach  a like  result  by 
a process  of  elimination.  If  we  have  given  several  possible 
explanations  of  a certain  situation  we  may  examine  each  in 
turn  and  prove  it  to  be  impossible,  and  so  narrow  the  range 
by  successive  elimination  until  one  only  is  left.  Negation 
becomes  especially  significant  when  there  are  but  two 
possibilities  in  reference  to  any  given  situation.  The  elimi- 
nation of  either  one  leaves  the  other  in  full  possession  of 
the  field.  Thus,  if  in  the  case  of  a murdered  man  it  can  be 
proved  negatively  that  he  never  had  an  enemy,  and  that 
there  was  no  one  who  would  have  sought  his  life  through 


VARIETIES  OF  JUDGMENT  FORMS 


83 


hatred  or  because  of  an  injury  received,  we  are  then  forced 
to  the  explanation  that  the  man  was  murdered  by  a burglar 
or  some  one  other  than  an  enemy.  This  process  of  elimina- 
tion by  negation  is  trustworthy  so  far  as  we  are  sure  that 
the  negative  judgment  is  true,  and  that  also  we  have  com- 
pletely embraced  all  possibilities  in  our  disjunction. 

We  have  seen  that  every  process  of  judgment  consists  in 
establishing  a unity  of  some  kind  among  the  elements  of  our 
thought.  Now  this  unifying  bond  in  judgment  admits  of 
a certain  degree  of  variability,  being  more  or  less  definite  in 
nature.  Its  degree  of  variability  determines  what  is  known 
as  the  modality  of  judgments. 

If  this  unifying  bond  is  actual,  the  judgment  is  known  as 
an  assertorical  judgment.  If  the  judgment  expresses  a pos- 
sible relation  only,  it  is  a problematical  judgment.  If  the 
judgment  expresses  a necessary  relation,  — that  is,  where  the 
unifying  bond  expresses  not  merely  that  which  is  but  that 
which  must  be,  — the  judgment  is  known  as  aoodeictic. 

The  categorical  judgment  naturally  takes  the  assertorical 
form,  e.g.  x is  y. 

The  disjunctive  judgment  naturally  takes  the  problemati- 
cal form,  e.g.  x may  be  y,  or  2,  or  w. 

The  hypothetical  judgment  naturally  take  the  apodeictic 
form,  e.g.  If  x is  y,  then  2 must  be  w. 

There  may,  however,  be  a change  of  modality  as  regards 
any  one  of  the  forms  of  judgment,  — categorical,  disjunctive, 
or  hypothetical.  Thus  the  categorical  judgment  will  be 
found  in  the  various  forms  as  follows : x is  y,  x may  be  y, 
x must  be  y.  The  first  of  these  is  the  natural  way  of  express- 
ing the  categorical ; for  the  form,  a;  may  be  y,  implies  other 
possibilities,  and  at  least  the  negative  possibility  that  x may 
not  be  y.  Therefore  the  problematical  mode  of  the  judgment 
is  to  be  regarded  as  implying  a disjunctive.  Moreover,  the 
categorical  form,  x must  be  y,  implies  a hypothetical  judg- 
ment as  its  basis,  for  the  assertion  of  necessity  naturally 
implies  some  knowledge  of  the  fundamental  relation  of 


84 


DEDUCTIVE  LOGIC 


ground  and  consequent  which  underlies  such  necessity. 
Thus  each  phase  of  modality  has  its  own  natural  form  of 
expression;  the  assertorical  expressing  itself  in  the  categori- 
cal judgment,  the  problematical  in  the  disjunctive,  and  the 
apodeictic  in  the  hypothetical. 


CHAPTER  X 


THE  NATURE  OF  INFERENCE 

The  nature  of  inference  may  be  unfolded  in  two  ways. 
We  may  consider  what  it  is  iu  its  outward  aspect ; that 
is,  through  its  phenomenal  manifestation  in  what  it  effects ; 
or  it  may  be  more  strictly  defined  in  terms  of  its  warrant 
or  ground.  From  the  first  point  of  view  we  examine  infer- 
ence as  regards  its  psychological  significance ; that  is, 
what  is  inference  considered  as  a psychical  experience,  its 
nature,  and  characteristics  ? But  we  must  consider  also  the 
second  question,  — whether  there  is  any  necessity  limiting 
and  determining  the  subjective  experience,  which  presents 
the  character  of  a law  having  universal  validity.  What 
goes  on  in  the  mind  during  the  process  of  inference  ? Also, 
what  is  the  rationale  of  such  a process  ? These  questions 
we  will  examine  more  closely,  in  order  to  show  the  nature 
of  inference  under  the  two  aspects,  the  one  psychological 
and  the  other  logical. 

It  is  a well-recognized  fact  in  psychology  that,  in  our 
simplest  as  well  as  the  more  complex  perceptions,  the  inter- 
pretation of  the  data  of  perception  always  goes  beyond  the 
strict  content  of  the  data  themselves.  We  see  more  than  is 
giveu  in  the  field  of  vision  immediately  before  us.  The  mind 
supplies  here  and  there  the  necessary  parts  that  are  lacking  in 
the  actual  elements  of  perception,  and  yet  which  are  necessi- 
tated by  the  known  nature  of  that  which  is  actually  given. 
We  form  our  judgment  of  distance  indirectly,  and  not  through 
direct  observation.  So,  also,  our  idea  of  a third  dimension  is 
acquired  by  a process,  marvellously  complex,  in  which  the 
data  both  indicate  and  yet  are  transcended  by  the  results. 
Whether  the  nativist  or  empiricist  holds  the  true  position 

85 


8G 


DEDUCTIVE  LOGIC 


concerning  original  psychical  experience,  it  still  must  be 
conceded  according  to  either  theory  that  the  development 
of  our  perceptions  corresponds  to  a law  of  growth  based 
upon  accumulated  inferences.  Inference  has  been  defined 
as  the  indirect  reference  of  a content  to  reality,  and  as  such 
we  see  the  beginnings  of  inference  in  the  most  simple  of  our 
perceptions.  Every  perception  contains  a direct  reference 
to  reality,  but  also  something  which  in  a greater  or  less 
degree  is  '-eferred  indirectly  to  reality.  The  fact  that  our 
knowledge  as  given  in  the  complete  perception  contains 
more  than  is  actually  mediated  through  the  avenues  of  the 
senses  is  due  to  the  apperceptive  processes  of  consciousness. 
Mind  is  active  in  perception,  and  not  a mere  passive  recep- 
tacle. That  which  is  given,  the  raw  material  of  the  senses, 
is  elaborated  and  extended,  as  it  is  combined  with  the 
wealth  of  representative  and  conceptual  material,  which 
the  mind  brings  to  every  new  perception.  To  this  extent, 
at  least,  the  mind  possesses  a creative  function.  A certain 
appearance  of  sky,  combined  with  peculiar  conditions  of 
wind  and  temperature,  leads  one  to  assert,  with  some  de- 
gree of  certitude,  that  it  will  rain  before  morning.  The 
prediction  is  an  inference  based  upon  and  growing  out  of 
the  actual  data  of  perception,  and  yet  far  outrunning  them. 
We  recognize  a friend  from  his  step  or  voice.  The  mere 
perception  is  only  a sound.  That  it  is  associated  with  a 
person,  and  not  an  animal,  or  a thing,  is  an  inference ; that 
it  is  the  particular  person  whom  we  recognize  as  a friend 
and  can  call  by  name,  even  before  we  turn  around  to  con- 
firm the  opinion  by  direct  testimony  of  vision,  this  is  a still 
further  inference.  And  even  when  we  open  our  eyes  in 
simple  vision  itself,  we  fill  up  many  a gap  in  our  minds, 
and  give  depth  and  distance,  and  interpret  the  contrasts 
of  light  and  shade,  and  the  play  of  colors,  through  the 
process  of  inference,  although  we  may  not  be  aware  of  the 
process  itself,  which  is  automatically  operative  through 
long-continued  habit.  When  we  thus  regard  inference  as 


THE  NATURE  OF  INFERENCE 


87 


a psychological  phenomenon,  it  may  be  readily  explained 
by  the  laws  of  comparison,  association,  recognition,  generali- 
zation, etc.  And,  as  such,  inference  has  a subjective  force, 
at  least,  and  leads  to  the  habit  of  prediction  and  expecta- 
tion. The  will,  influenced  by  the  resulting  belief,  leads 
to  activities  consistent  with  such  expectation. 

Here,  however,  the  question  arises  which  is  urged  with 
such  force  by  Hume,  Is  there  objective  validity  as  well  as 
subjective  necessity  ? This  leads  to  a consideration  of 
inference,  from  the  second  point  of  view,  above  mentioned. 
We  may  be  constrained  to  believe  certain  things  concerning 
the  great  world  lying  beyond  the  sphere  of  immediate  con- 
sciousness ; but  what  warrant  have  we  in  so  doing,  or  what 
assurance  that  our  conclusions  are  correct  ? May  we  not  be 
deceived,  after  all,  and  by  some  psychological  trick  be  led  to 
regard  the  phenomena  of  consciousness  as  quite  otherwise 
than  that  which  obtains  in  reality  ? We  may  have  a strong 
aversion  to  sitting  down  at  a table  where  the  number  of  per- 
sons will  be  thirteen.  But  has  the  subjective  conviction, 
that  one  of  the  thirteen  will  die  in  the  course  of  the  year, 
any  value  when  we  come  to  refer  it  to  reality,  and  ask  our- 
selves the  nature  of  the  ground  upon  which  the  conviction 
is  based  ? 

On  the  other  hand  however  it  is  quite  a different  kind  of 
necessity  which  constrains  us  to  judge  that  if  a person  jumps 
off  of  the  roof  of  a house,  he  must  surely  fall  to  the  ground 
below.  Some  grossly  superstitious  and  ignorant  people  may 
believe  the  former  with  as  obstinate  a conviction  as  the 
latter,  so  that  a purely  psychological  criterion  of  the 
strength  of  conviction  is  not  at  all  adequate  or  satisfactory. 
Is  there  any  other  criterion  ? In  what  instances  does  this 
subjective  constraint  proceed  from  the  necessities  of  reality  ? 
or,  in  other  words,  in  what  cases  are  we  able  to  discover  a 
logically  grounded  warrant  which  compels  the  inference,  in 
distinction  from  the  mere  psychological  compulsion  which 
is  occasioned  by  the  psychical  tendencies  of  association  and 
generalization  ? 


88 


DEDUCTIVE  LOGIC 


This  leads  us  to  consider  the  logical,  in  distinction  from 
the  psychological  nature  of  inference.  Inasmuch  as  the 
characteristic  feature  of  inference  consists  in  this,  that  while 
depending  upon  certain  data  of  perception,  it  nevertheless 
wholly  transcends  them,  the  question  naturally  suggests 
itself,  whether  it  is  something  within  the  data  themselves, 
cr  without,  by  virtue  of  which  the  mind  thus  goes  beyond 
them  in  the  process  of  inference.  If  it  lies  wholly  without 
the  data,  it  must  be  something  imposed  upon  them  by  the 
mind,  and  as  such  can  have  only  a psychological  force  and 
value.  For  instance,  the  belief  that  if  thirteen  sit  down 
together  at  a table,  one  will  die  in  the  course  of  the  year, 
can  have  only  a subjective  value  and  significance.  This  is 
true  in  all  cases  where  the  necessity  of  conviction  finds  its 
origin  in  prejudice  or  in  superstition,  or  it  may  be  in  the 
force  of  authority.  In  all  such  instances  we  feel  the  lack 
of  a satisfactory  logical  ground.  However,  on  the  other 
hand,  if  the  data  of  consciousness  contain  within  themselves 
that  which  enables  us  to  transcend  them  at  the  same  time 
that  we  interpret  them,  there  is  external  validity  for  our 
inference  that  has  a logical  worth.  This  seems  at  the  first 
glance  to  be  a paradox.  How  can  any  content  enable  us  to 
state  concerning  it  more  than  is  contained  within  it  ? The 
answer  to  the  seeming  paradox  is  that  every  concept,  and 
every  perception  as  well,  have  both  an  explicit  and  implicit 
content.  We  never  attain  complete  vision  or  perfect  appre- 
hension. 

There  are,  moreover,  many  points  of  view,  each  giving 
additional  knowledge  concerning  any  phenomenon  present 
in  consciousness.  We  see,  therefore,  only  in  part,  and  yet 
that  which  is  seen  contains  certain  necessary  implications 
concerning  that  which  is  not  seen.  In  the  progress  of 
knowledge,  subsequent  observations,  different  points  of 
view,  are  ever  confirming  and  amplifying  our  inferences, 
enabling  us  to  perceive  immediately  what  formerly  was  only 
inferred.  The  process  by  which  the  implicit  is  becoming 


THE  NATURE  OF  INFERENCE 


89 


explicit  indicates  a necessary  relation  existing  between  that 
which  is  known  mediately  and  that  which  is  known  imme- 
diately. Moreover,  consciousness  has  been  represented  as  a 
stream,  or  an  intricately  interwoven  web,  — something  ex- 
tremely complex.  Every  part  is  related  both  proximately 
and  remotely.  There  is  no  such  thing  as  an  isolated  per- 
ception ; every  perception  has  its  complex  relations  and 
connections.  So  also  every  concept  which  is  formed  by 
generalization  through  comparison  and  abstraction  of  our 
perceptions  as  interpreted  by  us,  possesses  this  character- 
istic of  greater  or  less  complexity.  In  this  manner  the 
world  of  consciousness  is  constructed,  that  is,  the  world  as 
it  is  for  us.  This  forms  a complex  whole  made  up  of  parts, 
which  in  themselves  may  be  regarded  as  wholes,  and  yet 
which  may  be  still  further  divided  and  subdivided. 

Such  an  interrelated  whole  we  may  style  a system,  or,  in 
other  words,  a complex  whole  whose  parts  are  congruently 
arranged.  The  idea  of  system  finds  expression  in  the  “ Law 
of  Totality,”  — that  our  knowledge  is  capable  of  arrange- 
ment in  a self-consistent  and  harmonious  system,  and  which 
moreover  in  its  content  and  form  faithfully  represents 
objective  reality.1  We  find,  therefore,  that  in  the  focus  of 
consciousness  at  any  one  time,  whether  in  the  sphere  of  per- 
ception or  in  the  region  of  representative  or  the  conceptual 
processes,  whatever  is  given  carries  with  it  always  certain 
implications,  and  therefore  certain  necessary  relations.  This 
is  specially  emphasized  in  Bosanquet’s  definition  of  system : 
“ System  is  a group  of  relations,  or  properties,  or  things,  so 
held  together  by  a common  nature  that  you  can  judge  from 
some  of  them  what  the  others  must  be.” 2 Two  facts  re- 
garded as  independent  and  considered  separately  may  give 
no  information  beyond  their  explicit  contents  ; but  when 
conjoined,  they  imply  more  than  the  sum  of  their  parts. 

1 Ueberweg,  A System  of  Logic  and  History  of  Logical  Doctrine,  pp. 
540  f. 

2 Bosanquet,  The  Essentials  of  Logic,  p.  140. 


90 


DEDUCTIVE  LOGIC 


How  often  two  ideas  in  separate  minds  yield  no  result ; but 
brought  together,  they  give  light.  Isolation  negatives 
inference.  To  unfold  whatever  is  given  in  all  its  manifold 
implications  is  the  process  of  inference.  Its  warrant  lies  in 
the  fundamental  postulate  of  knowledge  which  we  are  con- 
strained to  assume  ; namely,  that  our  consciousness  must  be 
self-consistent  throughout.  Whatever  is  admitted  as  true 
must  find  a congruent  place  in  the  system  to  which  it  is 
possible  to  refer  it.  The  necessity  of  fitting  it  in  its  proper 
place  gives  rise  to  certain  implications  which  necessitate 
corresponding  relations  and  attributes.  And  if  it  could  not 
be  put  into  such  a place,  we  would  feel  that  we  should  have 
to  surrender  the  idea  of  self-consistency  in  the  variously 
related  elements  of  our  consciousness.  The  very  integrity 
of  our  mental  life  necessitates  this  conviction. 

Therefore  a part  being  given,  we  supply  in  our  minds 
other  parts,  or  the  whole  to  which  the  given  part  must  nec- 
essarily belong.  To  achieve  this,  with  logical  warrant,  our 
knowledge  of  the  part  must  be  adequate  to  the  extent  that 
we  know  that  the  element  under  consideration  cannot  be 
complete  in  itself,  but  must  be  supplemented  by  its  appro- 
priately related  elements  which  with  it  go  to  make  up  the 
complete  system.  We  infer  the  nature  of  the  flower  not  yet 
in  bud  by  the  sprouting  leaf.  The  one  necessitates  the 
other  by  virtue  of  their  common  inherence  in  the  same  plant 
system.  We  know  that  figs  do  not  come  from  thorns  nor 
grapes  from  thistles.  Columbus,  noting  the  seaweed,  and 
birds,  and  the  drift  of  the  sea,  inferred  a shore  beyond,  to 
which  he  was  constrained  by  the  necessities  of  thought  to 
refer  them.  It  is  said  of  Cuvier  that  he  was  able  to  re- 
construct part  for  part  the  entire  frame  and  organism  of  an 
animal  whose  fossil  tooth  alone  formed  the  original  datum. 
He  knew  the  system  to  which  it  must  have  belonged  and  to 
which  it  alone  could  possibly  be  referred.  An  interesting 
quotation  from  Cuvier  himself  illustrates  most  appropriately 
this  function  of  inference.  He  says,  in  his  Ossemens  Fossilen : 


THE  NATURE  OP  INFERENCE 


91 


“ I doubt  if  any  one  would  have  divined,  if  untaught  by 
observation,  that  all  ruminants  have  the  foot  cleft,  and 
that  they  alone  have  it.  I doubt  if  any  one  would  have 
divined  that  there  are  frontal  horns  only  in  this  class ; that 
those  among  them  which  have  sharp  canines  for  the  most 
part  lack  horns.  However,  since  these  relations  are  con- 
stant, they  must  have  some  sufficient  cause ; but  since  we 
are  ignorant  of  it,  we  must  make  good  the  defect  of  the 
theory  by  means  of  observation : it  enables  us  to  establish 
empirical  laws  which  become  almost  as  certain  as  rational 
laws  when  they  rest  on  sufficiently  repeated  observations ; 
so  that  now  whoso  sees  merely  the  print  of  a cleft  foot  may 
conclude  that  the  animal  that  left  this  impression  ruminated, 
and  this  conclusion  is  as  certain  as  any  other  in  physics  or 
morals.  This  footprint  alone,  then,  yields  to  him  who 
observes  it  the  form  of  the  teeth,  the  form  of  the  jaws,  the 
form  of  the  vertebrae,  the  form  of  all  the  bones  of  the  legs, 
of  the  thighs,  of  the  shoulders,  and  of  the  pelvis  of  the 
animal  which  has  passed  by.”  1 

In  the  common  conduct  of  everyday  life  we  infer  beyond 
the  immediate  present  experience  to  future  happenings  and 
in  a similar  manner.  My  train  is  half  an  hour  late.  I 
know  I must  miss  my  connections  at  the  station  ahead  ; for 
the  train  I am  hoping  to  catch  at  that  place  is  scheduled  to 
leave  five  minutes  after  the  time  of  arrival  of  the  train  I am 
now  on.  The  time  relations  here  necessitate  my  missing 
my  connections.  This  is  rendered  still  more  certain  if  they 
are  rival  roads ; on  no  account  will  one  wait  for  the  other. 
Moreover,  the  train  I hope  to  make  is  made  up  and  leaves 
the  station  in  question,  and  so  I cannot  fall  back  upon  the 
favoring  chance  that  it  also  may  be  detained  en  route,  and 
so  enable  me,  after  all,  to  reach  it  in  time.  Thus,  with 
every  additional  knowledge  of  the  system  which  forms  the 
ground  of  my  inference,  and  the  various  conditions  which 
affect  it,  the  validity  of  my  inference  is  thereby  increased. 

1 Quoted  by  Jevons,  Principles  of  Science,  2d  ed.,  p.  683. 


92 


DEDUCTIVE  LOGIC 


Inference  regarded  as  the  analysis  of  a system  of  inter- 
related parts  is  illustrated  in  the  following  paragraph  of 
Professor  James  : “ The  result  of  reasoning  may  be  hit  upon 
by  accident.  Cats  have  been  known  to  open  doors  by  pulling 
latches,  etc.  But  no  cat,  if  the  latch  got  out  of  order,  could 
open  the  door  again,  unless  some  new  accident  at  random 
fumbling  taught  her  to  associate  some  new  total  movement 
with  the  total  phenomenon  of  the  closed  door.  A reasoning 
man,  however,  would  open  the  door  by  first  analyzing  the 
hindrance.  He  would  ascertain  what  particular  feature  of 
the  door  is  wrong.  The  lever,  e.g.,  does  not  raise  the  latch 
sufficiently  from  its  slot  — case  of  insufficient  elevation  — • 
raise  door  bodily  on  hinges  ! Or  door  sticks  at  top  by  fric- 
tion against  lintel  — press  it  bodily  down ! I have  a 
student’s  lamp  of  which  the  flame  vibrates  most  unpleas- 
antly unless  the  collar  which  bears  the  chimney  be  raised 
about  a sixteenth  of  an  inch.  I learned  the  remedy  after 
much  torment,  by  accident,  and  now  always  keep  the  collar 
up  with  a small  wedge.  But  my  procedure  is  a mere  asso- 
ciation of  two  totals,  diseased  object  and  remedy.  One 
learned  in  pneumatics  could  have  named  the  cause  of  the 
disease  and  then  inferred  the  remedy  immediately.”  1 

Inference,  therefore,  may  be  regarded  as  a deep  penetrat- 
ing insight.  The  explicit  is  that  which  lies  upon  the  surface, 
which  the  mind  immediately  grasps,  for  it  lies  directly  in 
the  focus  of  consciousness.  Whereas  the  implicit  is  beneath 
the  surface,  and  is  revealed  only  through  a searching  analy- 
sis. This  difference  may  be  exhibited  through  the  distinc- 
tion between  the  actual  and  the  potential.  A child  regards 
gunpowder  merely  as  a pile  of  coarse-grained  sand.  The 
man  sees  what  the  child  sees,  but  also  the  existing  possibili- 
ties under  certain  conditions  of  explosive  force.  He  appre- 
hends the  potential  as  well  as  the  actual ; and  his  inference 
as  to  the  possible  results  is  based  upon  his  superior  insight. 
It  is  therefore  the  well-furnished  mind  which  sees  things 
1 James,  Psychology,  Vol.  II,  pp.  339,  340. 


THE  NATURE  OF  INFERENCE 


93 


as  most  widely  related,  and  discerns  the  potential  as  well 
as  the  actual  manifestation,  which  will  prove  the  most 
fertile  in  accurate  inference,  in  prophetic  suggestion,  and 
in  inventive  resource. 

The  whole  world  of  reality,  as  well  as  that  of  knowledge, 
may  be  considered  as  one  system,  embracing  within  the 
unity  of  its  totality  all  the  various  systems  with  their  com- 
plicated parts.  From  this  point  of  view  everything  sustains 
relations  to  everything  else  in  the  universe.  The  original 
signification  of  the  term  universe  is  thus  emphasized.  This 
thought,  no  doubt,  Tennyson  had  in  mind  in  the  following 
verse : — 

Flower  in  the  crannied  wall, 

I pluck  you  out  of  the  crannies, 

I hold  you  here,  root  and  all,  in  my  hand, 

Little  flower  — but  if  I could  understand 
What  you  are,  root  and  all,  and  all  in  all, 

I should  know  what  God  and  man  is. 

We  can,  in  this  connection,  best  exhibit  the  precise  nature 
and  function  of  the  universal  in  inference.  The  possibility 
of  unfolding  the  properties  or  relations  of  anything  in  all 
its  implications  depends  upon  our  knowledge  of  the  univer- 
sal concept  to  which  the  properties  or  relations  in  question 
are  naturally  referred.  While  a singular  proposition  is  the 
statement  of  the  mere  occurrence  of  a phenomenon,  the 
universal  always  implies  a knowledge  of  the  conditions 
and  relations  of  the  phenomenon.1  Insight  is  only  possible 
where  there  is  a wealth  of  universal  concepts.  We  see  an 
animal  which  we  observe  to  be  cloven-footed.  We  infer 
that  it  also  chews  its  cud.  We  do  not  observe  this.  The 
assertion  does  not  arise  directly  from  observed  reality,  but 
indirectly  through  the  generic  concept  that  has  grasped  to- 
gether the  two  attributes,  of  chewing  the  cud  and  cloven 
feet  as  always  and  necessarily  coexisting  in  one  and  the 
same  animal.  Inference,  in  this  sense,  may  be  regarded 
1 See  Green,  Philosophical  Works , Yol.  II,  pp.  284,  285. 


94 


DEDUCTIVE  LOGIC 


as  the  indirect  reference  of  knowledge  to  reality,  and  this 
is  always  mediated  through  the  universal.  The  universal 
has  this  characteristic  feature,  that  it  preserves  an  identity 
in  the  midst  of  manifold  differences.  The  same  thought 
may  be  expressed  by  saying  that  the  universal  manifests 
a unity  in  the  midst  of  diversity.  However  widely  different, 
in  many  respects,  the  animals  may  appear  that  chew  the 
cud,  — as  the  cow,  deer,  sheep,  etc.,  — there  is  always  the 
constant  characteristic  that  they  are  cloven-footed. 

Such  a point  of  identity  furnishes  the  constant  factor 
which  determines  the  nature  and  the  validity  of  the  in- 
ference. Were  it  not  for  this  conceptual  power  of  the  mind, 
this  ability  to  grasp  phenomena  in  their  universal  essence, 
and  consider  them  as  interrelated  and  connected,  we  could 
never  pass  beyond  individual  and  particular  experiences 
which  would  form  a series  of  wholly  disconnected  events. 
Knowledge  could  not  then  form  a self-consistent  system, 
or  inference  possess  any  higher  worth  than  a haphazard 
guess.  As  Green  says,  “ A ‘ mere  fact,’  a fact  apart  from 
relations  which  are  not  sensible,  would  be  no  fact,  would 
have  no  nature,  would  not  admit  of  anything  being  known 
or  said  about  it.” 1 

Moreover,  inference  is  not  merely  employed  to  extend 
the  field  of  consciousness  in  unfolding  supple mentai’y  ele- 
ments lying  beyond  the  sphere  of  direct  cognition;  the 
elements  may  all  be  given  immediately,  and  inference  em- 
ployed to  discover  their  connection  and  interrelations,  and  by 
virtue  of  what  bond  they  belong  in  one  or  the  same  system. 
Inference  here  functions  as  explanation.  A man  is  found 
dead  ; there  are  many  wounds  upon  his  person,  and  evidences 
of  a struggle  in  an  out-of-the-way  place  upon  a lonely  road. 
Such  a combination  of  facts  calls  for  an  explanation  which 
shall  be  consistent  with  them.  The  facts  must  all  be  cor- 
related in  a system  whose  related  facts  and  the  unity  of 
the  whole  will  completely  satisfy  the  mind.  The  mind 
1 Green,  Philosophical  Works,  Vol.  II,  p.  301. 


THE  NATURE  OF  INFERENCE 


95 


is  satisfied  only  when  all  hang  together  in  what  seems  the 
only  possible  self-consistent  coordinated  system.  The  facts 
being  given,  they  must  be  read  backward  to  their  origin. 
The  other  aspect  of  inference  is  the  reading  of  facts  for- 
wards, or  unfolding  them  in  their  necessary  consequences. 
Inference  is  the  reply  to  the  natural  questions  of  the  mind, 
— whence  and  whither  ? And  the  process  is  essentially  the 
same,  whether  its  peculiar  mode  consists  in  the  evolution  or 
the  involution  of  that  which  is  given  in  consciousness. 

Moreover,  the  mere  psychological  inference,  the  subjective 
extension  of  the  data  of  consciousness  without  any  objec- 
tive ground  or  warrant,  should  ever  be  corrected,  or  even 
at  times  wholly  set  aside  by  means  of  the  truly  logical 
inference.  Where  the  psychological  experience,  in  tran- 
scending simple  presentation,  proceeds  upon  strictly  logical 
grounds,  and  has  objective  validity  as  well  as  subjective 
necessity,  we  possess  a warrant  of  the  highest  possible 
worth. 

The  relation  of  the  process  of  inference  to  that  of  judg- 
ment may  be  expressed  in  the  following  definition  that  in- 
ference is  a judgment  plus  the  reason  for  it.  Whenever  the 
reason  for  a judgment  is  obvious,  the  inferential  element 
falls  into  the  background.  The  judgment  then  appears 
merely  as  a restatement  of  a well-known  truth  which  no  one 
would  think  of  gainsaying,  or  as  the  result  of  referring  a 
familiar  object  of  perception  to  its  generally  recognized 
concept.  But  if  the  averred  truth  is  challenged,  or  if  the 
reference  of  the  perceived  object  is  not  clear,  then  in  order 
to  make  good  the  judgment,  recourse  must  be  had  to  some 
phase  of  the  inferential  process.  We  have  the  accepted 
judgment  that  lightning  is  a form  of  electrical  discharge. 
Such  a statement  commands  assent  without  question.  But 
when  Franklin  proved  the  identity  of  these  two  phenomena, 
it  was  by  a process  of  inference  in  which  it  was  necessary 
to  establish  the  common  ground  of  these  two  phenomena. 
If  one  should  point  to  a bird  circling  above  a field  in 


DEDUCTIVE  LOGIC 


96 


majestic  lines  of  flight,  and  say,  “That  is  an  eagle,”  the 
observation  would  probably  receive  immediate  assent.  It 
would  pass  then  as  an  obvious  judgment  of  perception. 

If,  however,  the  statement  should  meet  with  dissent,  or  an 
opposed  judgment  should  be  urged  that  it  is  a crow,  then 
the  inferential  element  revealing  the  necessary  ground  of 
the  judgment  would  at  once  come  to  the  fore.  It  would 
be  possible  to  point  out  that  the  flight  of  the  bird  is  so 
characteristically  the  flight  of  an  eagle  that  it  could  not  be 
mistaken  or  confused  with  that  of  a crow.  It  will  be  readily 
seen  that  the  inferential  element  is  contained  potentially 
in  every  judgment.  A direct  assertion,  received  without 
question,  is  the  judgment  in  its  simplest  form.  An  indirect 
statement,  showing  that  it  must  be  true  because  of  its  nec- 
essary connection  with  some  other  judgment,  is  an  inferred 
judgment.  In  the  light  of  this  distinction  the  difference 
between  judgment  and  inference  may  be  defined  as  fol- 
lows : — 

The  judgment  is  a direct  reference  of  a concept  to  reality. 

The  inference  is  an  indirect  reference  of  a concept  to 
reality. 

The  differentiating  line  is  evidently  a variable  one.  Its 
variability  depends  upon  the  presence  or  absence  of  any 
occasion  which  demands  a fuller  explication  of  the  ground 
of  a judgment.  As  long  as  the  ground  is  obvious  and  the 
judgment  unchallenged,  it  is  not  necessary  to  offer  any  proof 
of  it.  If  however  it  is  necessary  for  any  reason  to  give  an 
explicit  statement  of  the  ground  underlying  a judgment, 
then  at  once  the  inferential  element  passes  from  its  potential 
stage  into  its  developed  form  as  actually  expressed.  It  is 
often  the  opposition  of  a negative  judgment  which  provokes 
the  inferential  process  underlying  some  positive  assertion. 

Inference  may  be  deductive  or  inductive.  It  is  deductive 
when  the  process  shows  that  from  a universal  principle  or 
law  there  must  follow  some  special  case,  or  some  more 
special  phase  of  that  principle  or  law.  It  is  inductive  when 


THE  NATURE  OF  INFERENCE 


97 


the  process  shows  that  a general  principle  or  law  must  result 
from  the  investigation  of  special  cases. 

When  we  reason  that  a man’s  conduct  under  certain  given 
circumstances  will  be  honorable  or  dishonorable,  as  the  case 
may  be,  our  inference  is  based  upon  our  general  knowledge 
of  the  man’s  character,  and  the  inferential  process  is  one 
of  deduction.  When  however  we  reason  that  a man  must 
have  a certain  kind  of  character  in  the  light  of  a number  of 
particular  instances  which  we  have  observed,  our  inference 
is  based  upon  our  interpretation  of  these  special  cases  as  re- 
vealing an  underlying  universal  nature  which  we  call  the 
man’s  character.  Such  a process  is  one  of  induction.1 


1 See  Part  II,  Chapter  I,  on  “ Deduction  and  Induction.’ 


CHAPTER  XI 


THE  LAWS  OF  THOUGHT 

In  order  that  we  may  be  able  to  justify  our  judgments 
and  relate  them  to  each  other  and  to  the  main  body  of  our 
knowledge,  we  must  recognize  certain  fundamental  and 
universal  principles  known  in  logic  as  the  laws  of  thought. 
These  laws  are  as  follows : — 

1.  The  Law  of  Identity. 

2.  The  Law  of  Contradiction. 

3.  The  Law  of  Excluded  Middle. 

4.  The  Law  of  Sufficient  Reason. 

1.  The  law  of  identity  requires  every  concept  to  repre- 
sent some  phase  of  reality  which  remains  essentially  the 
same.  This  does  not  mean  an  identity  which  admits  of  no 
variety ; for  we  have  seen  that  it  is  of  the  very  nature  of 
the  concept  to  manifest  many  shades  of  difference  within 
the  variety  of  special  cases  which  illustrate  it.  It  does 
mean  however  that  in  spite  of  manifold  differences,  there 
is  a central  core  of  essential  identity  which  remains  con- 
stant and  unaffected  by  the  various  unessential  changes. 
This  law  has  been  formulated  in  the  simple  expression 
A = A.  Such  an  expression  is  true  but  meaningless,  and 
were  the  law  of  identity  restricted  to  such  an  expression  of 
it,  there  could  be  no  progress  in  thought,  for  every  judg- 
ment would  be  a mere  tautology  lacking  any  significance 
whatever.  The  law  would  be  more  exactly  formulated  by 
the  expressions  A = A!  = A"  = A"',  etc. ; that  is,  every  vari- 
ety of  A is  nevertheless  A,  or  every  special  case  of  A is  the 
same  as  every  other  special  case  of  A in  spite  of  all  differ- 

98 


THE  LAWS  OF  THOUGHT 


99 


ences.  This  law  therefore  is  merely  the  expression  of  the 
unity  which  is  the  ground  of  all  our  judgments.  Inasmuch 
as  inference  has  been  defined  as  the  reference  of  a judgment 
to  its  proper  ground,  then  this  law,  regarded  as  a law  of 
inference,  demands  that  such  ground  must  be  something 
abiding,  no  matter  what  variety  of  form  it  may  assume.  If 
the  ground  to  which  we  refer  a judgment  in  the  process  of 
inference  is  uncertain  and  shifting,  then  the  inference  itself 
is  invalidated.  Every  inference  therefore  requires  as  its 
ground  a relation  which  is  constant,  that  is,  identical  with 
itself. 

This  abiding  ground  which  gives  validity  to  our  infer- 
ence may  be  either  (1)  a single  thing  or  person  whose  self- 
identity  is  obviously  preserved,  or  (2)  it  may  be  a universal 
whose  very  nature  is  such  that  it  preserves  a unity  in  spite 
of  the  manifold  differences  in  the  various  instances  which 
illustrate  it.  As  an  example  of  inference  wherein  the 
identity  is  that  of  a single  person  there  is  the  story  of 
Thackeray’s  of  the  old  Abbe,  who,  one  day  conversing  with 
a party  of  intimate  friends,  chanced  to  say,  “ A priest  has 
strange  experiences;  why,  my  first  penitent  was  a mur- 
derer.” At  this  moment,  the  principal  nobleman  of  the 
neighborhood  enters  the  room.  “ Ah,  Abbe  ! here  you  are ; 
do  you  know,  ladies,  I was  the  Abbe’s  first  penitent,  and 
I promise  you  my  confession  astonished  him  ! ” The  two 
statements  of  the  Abbe  and  the  nobleman  become  signifi- 
cant solely  because  of  their  identity  of  reference  to  one  and 
the  same  individual.1  Again  in  the  case  wherein  the  identi- 
cal ground  is  not  an  individual  but  is  a universal,  a state- 
ment might  be  made  that  a certain  cloth  will  fade.  When 
asked  for  a reason,  the  reply  might  be,  because  that  cloth 
contains  a dye  which  always  does  fade.  It  is  evident  that 
the  validity  of  such  an  inference  depends  upon  the  constant 
nature  of  the  peculiar  kind  of  dye  in  question.  The  show- 
ing of  a universal  property  of  the  dye,  such  as  that  of  fading, 
1 This  illustration  is  taken  from  Bosanquet's  Essentials  of  Logic,  p.  140. 


100 


DEDUCTIVE  LOGIC 


forms  in  this  case  the  justifying,  ground  of  the  inference 
that  the  cloth  containing  the  dye  will  fade.  A true  uni- 
versal assures  an  identical  ground,  and  therefore  the  pos- 
sibility of  a constant  reference  as  completely  as  does  a 
single  individual. 

2.  The  law  of  contradiction  is  that  judgments  which  are 
opposed  to  each  other  (as  this  is  a,  and  this  is  not  a ; or  a 
is  b,  a is  not  b)  cannot  both  be  true.  The  truth  of  either 
one  renders  the  other  false.  This  is  essentially  the  axiom 
of  consistency.  It  serves  to  buttress  the  law  of  identity. 
The  latter  demands  the  preservation  of  a unity  in  spite  of 
differences.  The  law  of  contradiction  draws  a line  of  limi- 
tation as  a boundary  to  these  differences.  Beyond  such  a 
line,  the  differences  contradict  the  underlying  unity  which 
must  be  preserved  in  accordance  with  the  law  of  identity. 
It  prevents  the  reference  of  incompatible  properties  to  one 
and  the  same  subject  at  the  same  time  and  in  the  same  sense. 

The  law  of  contradiction  applies  to  judgments  which  are 
opposed  in  a contrary  as  well  as  a contradictory  manner. 
The  contradictory,  it  will  be  remembered,  is  the  general 
term  for  the  total  area  of  negation  lying  outside  the  defin- 
ing boundary  of  the  positive  term  to  which  it  is  opposed. 
The  contrary  is  any  special  case  of  the  contradictory  which 
may  be  designated  by  a part  of  the  area  of  total  negation. 
The  judgments  a is  b,  a is  not  b,  are  contradictorily  opposed. 
The  judgments  a is  b,  a is  c,  are  contrarily  opposed  when- 
ever c is  any  property  incompatible  with  b.  To  such  judg- 
ments the  law  of  contradiction  also  applies ; if  it  is  true  that 
a is  b,  then  the  statement  that  a is  c must  be  false. 

We  have  seen  that  a bare  denial  as  in  contradictory  oppo- 
sition is  not  significant,  and  that  significant  denial  rests 
upon  the  knowledge  of  some  property  or  relation  which  is 
contrary  to  the  alleged  assertion  which  it  opposes.  Most 
of  our  denials,  therefore,  are  contrary  rather  than  contradic- 
tory. Inconsistencies  arise  in  thought  more  often  by  the 
endeavor  to  unite  properties  slightly  contrary  than  those 


THE  LAWS  OF  THOUGHT 


101 


wholly  contradictory.  Controversies  which  take  the  form, 
It  is,  It  isn’t,  and  are  conducted  by  continued  reiteration 
of  bare  assertion  and  denial,  are  always  meaningless  and 
futile.  If  a statement  is  made  that  a certain  ore  is  gold, 
we  may  deny  it  merely  by  saying  it  is  not.  This  is  contra- 
dictory opposition.  We  may  say  also,  It  is  iron  pyrites, 
i.e.  a special  case  of  that  which  is  not  gold.  The  denial 
is  significant  and  represents  contrary  opposition.  The  law 
of  contradiction  applies  equally  to  the  two  cases.  If  the 
statement,  It  is  gold,  is  true,  then  both  of  the  following 
statements  are  negatived : It  is  not  gold ; also  it  is  iron 
pyrites. 

3.  The  law  of  excluded  middle  is,  that  between  two 
judgments  contradictorily  opposed  there  is  no  middle  or 
third  judgment  which  is  true.  One  or  the  other  of  the 
two  given  judgments  must  be  true.  This  law,  however, 
does  not  apply  to  judgments  which  express  contrary  oppo- 
sition, for  it  is  of  the  very  nature  of  contraries  that  there 
is  middle  ground  between  the  extremes  which  they  repre- 
sent. Both  statements,  x is  greater  than  y,  x is  less  than 
y,  may  be  false,  because  of  the  middle  possibility  x=y. 
However,  contrary  statements  in  the  light  of  special  circum- 
stances which  render  them  an  exhaustive  disjunction  come 
under  the  law  of  excluded  middle,  e.g.  He  had  either  to 
jump  from  the  window,  or  perish  in  the  flames.  The  cir- 
cumstances were  such  as  to  leave  no  other  course  open.  A 
contrary  relation  within  a limited  universe  of  discourse 
thus  ranks  as  a contradictory  relation  because  the  limita- 
tion of  the  area  of  relevant  subject-matter  cuts  out  a 
middle  ground  which  in  an  unlimited  universe  of  thought 
might  otherwise  appear.  Much  of  the  loose  thinking, 
especially  in  untrained  and  unreflecting  minds,  arises  from 
the  careless  assumption  of  contradictory  alternatives,  when 
in  reality  they  are  merely  contrary.  The  middle  ground 
is  overlooked,  and  logical  confusion  inevitably  results. 
The  law  of  excluded  middle  always  secures  an  exhaustive 


102 


Deductive  logic 


disjunction,  and  therefore  renders  a negative  statement 
significant  inasmuch  as  the  other  and  opposed  alternative 
is  then  necessarily  true. 

4.  The  law  of  sufficient  reason  is  that  every  judgment 
must  be  based  upon  some  satisfactory  ground  which  fully 
justifies  it.  This  law  was  first  formulated  by  Leibniz 
(1646),  and  placed  by  him  side  by  side  with  the  law  of 
contradiction.  It  is  so  intimately  associated  with  the 
great  philosopher  that  it  would  be  worth  while  to  have 
his  own  statement  of  it.  “Our  intellectual  inferences  rest 
on  two  great  principles:  the  principle  of  contradiction,  and 
the  principle  of  sufficient  reason,  in  virtue  of  which  we 
know  that  no  fact  can  be  found  real,  no  proposition  true, 
without  a sufficient  reason  why  it  is  in  this  way  rather 
than  in  another.”  This  law  is  essentially  the  statement  of 
the  fundamental  logical  basis  upon  which  all  inference 
rests,  namely,  that  our  knowledge  forms  a system  of  inter- 
related and  coordinated  parts,  and  that  any  single  element 
can  be  determined  only  when  its  relation  is  known  to  some 
other  element  or  elements  upon  which  it  depends.  It  is 
a law  which  recognizes  a reciprocal  dependence  of  part  to 
part  throughout  the  entire  body  of  knowledge.  It  is  a 
corollary  of  this  law  that  every  judgment  contains  a poten- 
tial inference ; for  every  judgment  is  true  in  so  far  as  it  is 
based  upon  a sufficient  ground,  and  to  render  explicit  the 
ground  upon  which  it  rests  is  itself  the  process  of  inference. 

In  these  four  laws  we  find  that  certain  logical  demands 
are  made  to  which  all  processes  of  thought  must  adhere. 
The  law  of  identity  demands  a basis  of  constant  reference", 
the  law  of  contradiction,  that  of  consistent  treatment ; the 
law  of  excluded  middle,  that  of  an  exhaustive  survey  of 
possibilities ; and  the  law  of  sufficient  reason,  that  of  ade- 
quate explanation.  There  are  many  rules  which  are  given 
for  guidance  in  the  various  processes  of  inference,  which, 
however,  are  merely  adaptations  of  some  one  or  other  of  the 
several  phases  of  these  four  fundamental  principles. 


CHAPTER  XII 


IMMEDIATE  INFERENCE 

In  the  traditional  logic  the  distinction  is  drawn  between 
immediate  and  mediate  inference,  the  former  being  the  di- 
rect reference  of  a judgment  to  its  ground,  the  latter  the 
indirect  reference  of  a judgment  to  its  ground  through  the 
medium  of  one  or  more  intervening  judgments.  Such  a dis- 
tinction, however,  will  not  hold.  All  inference  is  indirect. 
Indeed  inference  is  defined  as  the  indirect  reference  of  a 
concept  to  reality.  The  difference  between  the  so-called 
immediate  and  mediate  inference  is  rather  one  of  degree. 

In  the  immediate  inference  from  a given  proposition  in  the 
form,  All  x is  y,  to  the  derived  proposition,  Some  x is  y,  the 
process  is  not  as  direct  as  it  seems.  It  assumes,  tacitly  at 
least,  another  mediating  judgment  that  whatever  is  true  of 
a class  generically  is  true  of  every  member  of  the  class,  — 
the  old  Aristotelian  dictum.  Such  a judgment  as  this,  how- 
ever, is  so  obvious  that  it  falls  into  the  background,  and 
the  inference  seems  to  be  immediate.  Immediate  inference, 
therefore,  may  be  regarded  as  an  abbreviated  form  of  infer- 
ence in  general.  The  term  “ immediate  reference,”  however, 
in  the  history  of  logic,  is  not  applied  to  any  inference  what- 
ever which  employs  an  obvious  mediating  judgment,  but  it 
is  restricted  to  certain  definite  aspects  of  inference  dependent 
upon  general  considerations  of  a self-evident  character. 
These  considerations  give  rise  to  two  well-defined  types  of 
immediate  inference  according  as  the  process  is  one  of 
implication  or  transformation. 

1.  The  process  of  implication  depends  upon  the  funda- 
mental relations  which  exist  between  “all”  and  “some”  and 

103 


104 


DEDUCTIVE  LOGIC 


between  “yes”  and  “no”;  that  is,  if  we  have  a judgment,  for 
instance,  in  the  form  of  a universal  affirmation,  all  are,  what 
is  implied  in  reference  to  the  particular  affirmation,  some 
are,  or  the  universal  negative,  none  are,  or  the  particular 
negative,  some  are  not?  The  possible  combinations  which 
we  are  able  to  make  with  the  terms,  “all,”  “some,”  “none,” 
“ some  not,”  give  us  four  distinct  types  of  judgment  which 
for  convenience  of  reference  are  designated  by  the  four 
vowels  A,  E,  I,  and  0 as  follows : — 

A — The  Universal  Affirmative  ; All  x is  y. 

E = The  Universal  Negative ; No  x is  y. 

I = The  Particular  Affirmative ; Some  x is  y. 

0 = The  Particular  Negative ; Some  x is  not  y. 

Judgments  which  differ  as  universal  and  particular  are 
said  to  differ  in  quantity ; those  which  differ  as  affirmative 
and  negative  are  said  to  differ  in  quality.  It  will  be  seen 
that  the  question  of  the  various  implications  involved  in  the 
relations  which  these  several  kinds  of  judgment  sustain  to 
one  another,  is  a general  question  which  has  to  do  with  the 
significance  of  the  forms  which  all  our  judgments  assume, 
whatever  may  be  their  content;  for  any  judgment  concern- 
ing any  object  of  knowledge  must  be  put  in  one  or  another 
of  these  four  forms. 

Now  if  a judgment  in  any  one  of  these  four  forms  is  given 
as  true,  certain  necessary  implications  will  follow  in  refer- 
ence to  the  other  three.  Likewise,  if  any  judgment  is  given 
as  false,  certain  necessary  implications  will  follow. 

In  order  to  exhibit  these  relations  in  as  clear  a manner  as 
possible,  Aristotle  devised  the  scheme  of  placing  the  four 
kinds  of  judgment  each  at  a corner  of  a square,  known  as  the 
Aristotelian  square,  or  the  square  of  opposition.  The  latter 
term  is  misleading,  however,  as  all  the  relations  are  not 
opposed,  but  only  those  obtaining  between  affirmation  and 
negation.  A better  term,  which  covers  all  the  possible  rela- 
tions, is  implication.  The  judgments  are  arranged  about 


IMMEDIATE  INFERENCE 


105 


the  square  so  that  the  universals  are  above,  the  particulars 
beneath,  the  affirmatives  at  the  left,  and  the  negatives  at  the 
right.  This  arrangement  will  give  us  the  following : — 


THE  SQUARE  OF  ARISTOTLE 

All  xisy  • No  x is  y 

A Contrary  E 


In  the  above,  the  word  “ some  ” is  to  be  regarded  as  equiv- 
alent to  “ some  at  least.”  In  the  proposition,  Some  x is  y, 
there  is  no  indication,  as  far  as  the  bare  form  is  concerned, 
whether  it  may  not  also  be  true  that  All  x is  y,  or,  on  the 
other  hand,  that  Some  x is  not  y.  “ Some,”  used  in  this 
sense,  is  the  “ some  ” of  preliminary  investigation,  wherein  a 
connection  has  been  established  between  x and  y,  but  the  in- 
vestigation is  not  fully  complete.  Upon  further  research,  it 


106 


DEDUCTIVE  LOGIC 


may  be  that  exceptions  will  be  found  which  might  render  a 
generalization  impossible,  or  it  may  be  that  the  connection 
can  be  so  firmly  established  as  to  admit  of  a generalization 
as  regards  its  logical  force.  “ Some,”  in  this  sense,  lies  be- 
tween the  terms  “ all  ” and  “ some  only,”  and  is  equivalent 
to  “ some  at  least.” 

Now,  as  regards  the  various  relations  which  this  diagram 
illustrates,  there  are  the  following : — 

1.  The  subaltern  relation  between  the  universal  (either 
affirmative  or  negative)  and  its  corresponding  particular  is 
so  called  because  the  particular  is  regarded  as  being  subor- 
dinated to  the  universal.  The  relation  between  universal 
and  particular  is  such  that  if  the  universal  is  true,  the  par- 
ticular is  true  also ; but  if  the  particular  is  true,  the  truth 
of  the  universal  is  left  in  doubt.  The  truth  of  a particular 
judgment,  as  based  upon  the  truth  of  the  corresponding  uni- 
versal, follows  from  our  fundamental  law  of  identity,  that 
the  universal  preserves  its  essential  unity  in  all  the  particu- 
lar forms  of  its  manifestation.  The  indeterminateness  of  the 
universal,  when  the  particular  is  given  as  true,  is  due  to 
the  possibility  that  the  connection  expressed  by  the  particu- 
lar judgment  in  question  may  be  accidental,  and  therefore 
not  a part  of  the  essential  content  of  the  species  as  a whole. 

Moreover,  if  the  universal  is  false,  the  particular  is  left  in 
doubt.  It  may  be  true  or  false,  according  to  the  concrete 
circumstances  in  any  given  case.  The  reason  for  this  is 
that  the  bare  denial  of  a universal  is  always  ambiguous.  It 
may  be  a total  denial  by  confronting  it  with  the  opposite 
universal,  or  it  may  be  a partial  denial  by  pointing  out 
exceptions  to  it ; which,  of  course,  render  the  affirmed  uni- 
versality false.  But  the  falsity  of  a particular  renders  its 
corresponding  universal  false;  for,  if  the  particular  state- 
ment is  not  true,  much  less  will  be  the  universal,  which 
embraces  the  particular  under  it. 

2.  The  contrary  relation  between  A and  E propositions  is 
such  that  if  either  of  the  related  judgments  is  true,  the  other 


IMMEDIATE  INFERENCE 


107 


must  be  false,  but  if  either  is  false,  the  other  is  indeter- 
minate. For  it  is  obvious  that  between  “ all  ” and  “ none  ” 
there  is  middle  ground,  and  therefore  they  are  related  as  con- 
traries ; and  it  is  the  nature  of  the  contrary  relation  that, 
according  to  the  law  of  contradiction,  the  truth  of  one  ren- 
ders the  other  false ; and,  as  there  is  middle  ground  between 
them,  the  law  of  excluded  middle  does  not  apply,  and  there- 
fore the  fact  that  one  is  false  merely  leaves  the  other  inde- 
terminate. 

3.  The  subcontrary  relation  between  I and  0 is  the  inverse 
of  the  contrary.  Here  the  falsity  of  either  renders  the  other 
true,  but  the  truth  of  either  leaves  the  other  indeterminate. 
This  is  perhaps  more  difficult  to  see.  It  should  be  remem- 
bered that  “ some  ” = “ some  at  least.”  Now,  if  it  is  false  that 
Some  x is  y,  it  must  be  true  that  Some  x (at  least)  is  not  y, 
which  latter  statement  is  not  incompatible  with  the  fuller 
statement  that  No  x is  y,  for  it  is  merely  a special  case  under 
it.  But  if  it  is  true  that  Some  x (at  least)  is  y,  we  have  seen 
that  by  the  very  significance  of  “ some  ” thus  interpreted, 
the  question  as  to  whether  there  may  be  exceptions  ex- 
pressed in  the  form  Some  x is  not  y is  left  in  doubt. 

4.  The  contradictory  relations  between  A and  0 and 
between  E and  / are  such  that  if  either  is  true,  the  other  is 
false,  and  if  either  is  false,  the  other  is  true.  This  follows 
directly  from  the  law  of  excluded  middle.  That  the  propo- 
sitions, All  x is  y,  and  Some  x is  not  y,  have  no  middle 
ground  between  them  is  evident.  It  may  be  put  in  this 
way : if  a judgment  is  always  true,  it  admits  of  no  excep- 
tions, and  if  it  has  exceptions,  it  is  not  always  true ; if  a 
judgment  is  not  always  true,  it  must  have  exceptions,  and  if 
it  does  not  have  exceptions,  it  must  be  always  true. 

These  relations  may  be  summarized  as  follows : — 

1.  Given  A true,  then  I is  true,  the  others  false. 

2.  Given  E true,  then  0 is  true,  the  others  false. 

3.  Given  A false,  then  0 is  true,  the  others  unknown. 


108 


DEDUCTIVE  LOGIC 


4.  Given  E false,  then  I is  true,  the  others  unknown. 

5.  Given  I true,  then  E is  false,  the  others  unknown. 

6.  Given  0 true,  then  A is  false,  the  others  unknown. 

7.  Given  I false,  then  A is  false,  the  others  true. 

8.  Given  0 false,  then  E is  false,  the  others  true. 

These  eight  statements  may  be  still  further  condensed  as 
follows : — 

I.  Given  A or  E true,  I or  0 false,  the  corresponding 
subaltern  is  the  same,  the  others  opposite. 

II.  Given  A or  E false,  I or  0 true,  the  corresponding 
contradictory  is  opposite,  the  others  unknown. 

There  are  two  practical  suggestions  which  emerge  from 
these  dry  symbols,  which  may  prove  not  only  interesting 
but  also  of  some  value.  (1)  The  one  is  that  the  trend  of 
logical  thought  is  always  from  the  universal  to  the  particu- 
lar, from  “ all  ” to  “ some,”  and  that  procedure  in  the  oppo- 
site direction  is  one  of  the  most  fertile  sources  of  error  in 
thinking.  It  is  the  well-known  fallacy  of  hasty  generali- 
zation, namely,  the  collecting  of  a few  instances  of  experi- 
ence and  immediately  raising  them  to  the  rank  of  a 
universal.  There  is  no  procedure  of  thought  which  needs 
to  be  so  carefully  safeguarded  as  that  from  “ some  ” to 
“all.”  (2)  Again  there  is  the  principle  which  I would 
call,  the  economy  of  refutation.  It  is  this : Whenever  in 
discussion  or  debate  a universal  judgment  is  advanced,  do 
not  attempt  to  controvert  it  by  the  opposite  universal,  but 
rather  by  the  opposite  particular.  There  will  be  less  diffi- 
culty in  proving  a particular,  and  thus  a strategic  point  of 
advantage  will  be  gained.  If  a proposition  is  advanced  in 
the  form  All  x is  y,  to  refute  it,  it  is  only  necessary  to  prove 
essential  exceptions  in  the  form  of  Some  x is  not  y.  Thus 
in  the  Harvard-Princeton  debate  in  1896,  the  question  was, 
Resolved  that  Congress  should  take  measures  to  retire  all 
the  legal  tender  notes.  Princeton  maintained  the  affirm  a- 


IMMEDIATE  INFERENCE 


109 


tive.  Harvard’s  attack  upon  this  position  was  not,  as  might 
have  been  expected,  a universal  negative,  — namely,  that  no 
legal  tender  notes  should  be  retired  by  Congress,  — but  a 
particular  negative,  that  not  all  but  only  some  should  be 
retired.  It  is  a useful  rule  to  remember  in  debate, — 
never  attempt  to  prove  more  than  is  necessary  to  overthrow 
your  opponent’s  main  contention. 


CHAPTER  XIII 


ON  TRANSFORMATIONS  OF  JUDGMENT  FORMS 

The  different  forms  of  judgment  may  be  subjected  to 
various  changes,  some  of  which  give  slightly  new  shades  of 
meaning,  without  however  altering  the  logical  force  of  the 
judgment  itself.  The  original  judgment  and  its  transfor- 
mation must  be  logically  compatible.  This  is  the  criterion 
by  which  all  transformations  are  to  be  tested.  These  trans- 
formations may  be  produced  in  various  ways : by  an 

interchange  of  subject  and  predicate;  by  a change  in  the 
quantity  or  quality1  of  the  judgment;  by  the  change  of  a 
term  to  its  contradictory;  or  by  certain  complex  changes 
involving  all  of  these. 

The  interchange  of  subject  and  predicate  is  called  the 
Conversion  of  a proposition. 

If  it  is  a proposition  of  the  A form,  All  x is  y,  its  simple 
conversion  will  give  All  y is  x.  This,  however,  alters  the 
logical  force  of  the  original  proposition ; for,  if  we  have 
given  the  form  All  x is  y,  it  maj^  be  that  the  predicate  y is 
the  common  mark  of  a number  of  species  besides  x,  such  as 
x,  z,  w,  etc.  Therefore,  y is  not  a distinctive  mark  of  x at 
all,  and  it  does  not  follow  that  because  All  x is  y,  therefore 
All  y is  x.  In  the  conversion  of  an  A proposition  the  uni- 
versal force  is  lost,  and  only  a particular  is  possible.  Thus 
All  x is  y becomes  Some  y is  x.  This  is  called  conversion  by 
limitation,  or  conversio  per  accidens. 

With  the  universal  negative,  however,  No  x is  y,  a simple 
conversion  is  possible,  because  the  negative  asserts  a com- 
plete incompatibility  of  x and  y,  and  such  being  the  case,  it 
is  a matter  of  indifference  whether  we  say  that  x cannot  be 

1 See  page  104. 

110 


TRANSFORMATIONS  OF  JUDGMENT  FORMS  111 


fused  into  any  unity  with  y,  or  that  y cannot  be  fused  into 
any  unity  with  a;.  Thus  No  x is  y becomes  by  conversion 
No  y is  x. 

With  the  particular  affirmative  form,  Some  x is  y,  a simple 
conversion  into  Some  y is  a;  is  also  possible,  because  if 
some  x forms  a unity  with  y,  some  y at  least  must  be  pres- 
ent with  x to  constitute  that  unity.  Thus  Some  x is  y 
becomes,  by  conversion,  Some  y is  x. 

But  with  the  particular  negative,  Some  x is  not  y,  the 
simple  conversion  Some  y is  not  x does  not  necessarily 
follow;  for  the  subject  y may  represent  a species  and  the 
predicate  x its  corresponding  genus.  Obviously,  Some  y 
is  not  x will  be  false,  for  the  species  must  fall  wholly 
within  its  corresponding  genus.  Thus  if  we  have  a judg- 
ment of  this  kind  such  as,  Some  reptiles  are  not  snakes, 
and  convert  it,  we  get  Some  snakes  are  not  reptiles,  which 
is  obviously  false.  Thus  a particular  negative  cannot  be 
converted. 

The  possibilities  of  conversion  may  be  summarized  as 
follows : — 


The  above  are  the  only  transformations  which  are  pos- 
sible when  we  regard  the  form  of  the  propositions  merely. 
If,  however,  in  addition  to  their  mere  formal  structure,  we 
take  into  consideration  their  content,  — that  is,  the  meaning 
of  the  subject  and  predicate  terms  and  their  relation  to  each 
other  in  any  judgment,  — then  a greater  range  in  conversion 
is  possible. 

Thus,  in  the  universal  affirmative,  if  the  subject  and 
predicate  are  coextensive  terms,  or  if  they  are  coordinate 
properties  of  the  one  and  the  same  concept,  then  a simple 
conversion  without  change  is  possible.  Given,  All  equian- 


Con  verted 


Given 


A All  x is  y . . . . 

E No  x is  y . . . . 

I Some  x is  y . . . . 

0 Some  x is  not  y . . 


I Some  y is  x 
E No  y is  x 
I Some  y is  x 


No  result 


112 


DEDUCTIVE  LOGIC 


gular  triangles  are  equilateral.  By  conversion  we  have  All 
equilateral  triangles  are  equiangular. 

Or  if  the  universal  proposition  is  in  the  form  of  a defini- 
tion,— i.e.  a concept  referred  to  its  genus  and  differentia, — 
then  simple  conversion  is  possible.  Democracy  is  govern- 
ment by  the  people.  A government  by  the  people  is  a 
democracy.  It  is  evident  that  an  indefinite  reference  of  a 
concept  to  a class  genus  merely,  or  a description  of  a concept 
by  one  or  more  of  its  attributes,  will  give  a proposition 
which  admits  of  conversion  only  by  limitation,  i.e.  change 
of  “ all  ” to  “ some  ” ; but,  on  the  other  hand,  a definite  refer- 
ence which  serves  to  differentiate  the  concept  in  question 
admits  of  simple  conversion. 

The  same  observation  applies  to  the  conversion  of  a 
hypothetical  judgment.  Given  a judgment  of  the  form, 
If  x is  y,  z is  w,  it  does  not  follow  that  if  z is  w,  x is  y ; for 
there  may  be  other  antecedents  which  will  give  us  z is  w, 
as  well  as  the  given  one  x is  y.  Thus,  given  the  judgment, 
If  the  democrats  win,  they  must  carry  New  York  State, 
it  does  not  follow  that  if  they  carry  New  York  State,  they 
will  win. 

It  is  the  aim  of  all  exact  thinking,  of  all  scientific  formu- 
lation especially,  to  render  thought  so  definite  that  a simple 
conversion  is  possible.  It  is  not  sufficient  to  refer  a species 
to  a genus,  which  is  a class  embracing  also  many  other 
species,  but  to  so  refer  the  species  in  question  by  means  of 
its  differentiating  properties,  that  the  reference  will  become 
distinctive.  Moreover,  while  a given  consequent  may  follow 
from  many  antecedents,  it  is  the  aim  of  exact  thinking  to 
connect  certain  specific  marks  which  accompany  that  con- 
sequent with  certain  causal  conditions  present  in  some  one 
of  the  many  possible  antecedents  and  not  present  in  the 
others.  Simple  conversion  is  then  of  course  possible. 

Logical  error  arises  when  judgments  expressing  inexact 
references  are  converted  simply  by  unreflecting  persons. 
As,  for  instance,  when  an  ignorant  foreigner  reasons  that  be- 


TRANSFORMATIONS  OF  JUDGMENT  FORMS  113 


cause  all  travellers  who  give  unusually  large  tips  are  Ameri- 
cans, that  therefore  all  Americans  will  give  unusually  large 
tips.  The  error  is  more  apt  to  arise  when  subject  and  predi- 
cate, or  antecedent  and  consequent,  approach  very  near  the 
boundary  of  simple  conversion,  but  have  not  quite  reached 
it.  The  margin  is  so  narrow  however  that  it  is  overlooked, 
and  error  naturally  results.  Thus,  no  one  would  think  of 
converting  the  proposition,  All  United  States  Senators 
are  members  of  Congress,  into  All  members  of  Congress 
are  United  States  Senators,  but  many  might  fall  into  the 
fallacy  of  converting  the  proposition,  All  the  democrats 
in  the  Senate  voted  against  the  bill,  into  All  Senators  who 
voted  against  the  bill  were  democrats. 

The  wider  range  of  conversion  which  is  rendered  possible 
by  the  consideration  of  content  in  addition  to  that  of  form 
merely,  may  also  be  illustrated  in  the  particular  affirmative, 
Given,  Some  x is  y ; then,  if  it  is  known  in  addition  that  y 
is  a species  of  x,  we  may  convert  the  particular  into  a 
universal,  and  get  All  y is  x as  the  result.  Thus,  if  we 
have  given  the  judgment  that  Some  birds  of  prey  are  vultures, 
we  can  convert  it  so  as  to  obtain  All  vultures  are  birds  of 
prey. 

Again,  in  the  particular  negative,  conversion,  which  is  not 
possible  by  consideration  of  form  alone,  becomes  possible 
if,  on  examination  of  content,  we  know  that  the  predicate 
is  not  a species  of  the  subject.  Thus,  if  we  have  given  Some 
birds  of  prey  are  not  hawks,  we  can  convert  it  into  Some 
hawks  at  least  are  not  birds  of  prey.  But  if  the  predicate  is 
a species  of  the  subject,  conversion  is  impossible,  e.g.  Some 
governments  are  not  republics.  The  relation  of  form  to 
content  is  such  in  general  that  not  merely  is  it  impossible 
to  interpret  the  full  significance  of  a proposition  without 
knowing  its  content,  but  also  it  is  impossible  to  assent  to 
any  formal  statement  whatsoever  unless  we  know  in  addition 
the  significance  of  the  terms  used.  The  proposition,  All  x 
is  y,  is  a mere  skeleton  form,  but  in  the  actual  judgments 


114 


DEDUCTIVE  LOGIC 


of  our  thinking  x and  y are  replaced  by  definite  concepts 
with  a real  significance.  Our  first  thought,  therefore,  is 
whether  the  real  concepts  which  we  substitute  for  x and  y 
in  our  symbolic  form  will  admit  of  a universal  affirmative 
assertion,  or  of  a universal  negative,  etc.  Form  without 
content  is  meaningless ; content  without  form  is  confusion. 
The  one  is  always  a function  of  the  other. 

We  come  now  to  a second  kind  of  transformation,  known 
as  Obversion.  It  consists  in  a change  in  the  quality  of  a 
proposition  from  affirmative  to  negative,  or  from  negative  to 
affirmative,  and  at  the  same  time  a compensating  change  of 
the  original  predicate  to  its  corresponding  contradictory. 
If  the  original  proposition  is  true,  a single  change  of 
quality  would  render  the  transformed  proposition  false, 
therefore  the  predicate  term  is  changed  by  way  of  com- 
pensation, because  the  reference  of  any  predicate  to  a sub- 
ject has  the  same  logical  force  as  that  of  excluding  the 
contradictory  of  that  predicate  from  the  same  subject. 
Given,  All  such  conditions  are  impossible,  by  obversion  we 
have  No  conditions  of  such  a nature  are  possible.  The 
same  process  holds  in  the  obversion  of  the  other  forms 
of  judgment,  and  we  have  the  following  tabulated  sum- 
mary : — 


Given 


All  x is  y A 

No  a;  is  y E 

Some  x is  y I 

. Some  x is  not  y O 


Obverted 

No  a;  is  not-?/  E 
All  x is  not -y  A 
Some  x is  not-?/  0 
Some  x is  not-?/  I 


The  term  “not-?/”  is  usually  expressed  by  some  form  of  a 
negative  affix  such  as  impossible,  ?«icontrollable,  etc. 

There  are  several  complex  transformations  formed  by 
the  combined  processes  of  conversion  and  obversion.  Of 
these  the  so-called  Contrapositive  is  formed  by  subject- 
ing the  given  proposition  to  three  transformations,  as  fol- 
lows : — 


TRANSFORMATIONS  OF  JUDGMENT  FORMS  115 


1.  Obversion. 

2.  Conversion. 

3.  Obversion. 

Given  the  proposition : All  scholarly  work  is  logical, 

1.  By  obversion,  No  scholarly  work  is  illogical. 

2.  By  conversion,  No  illogical  work  is  scholarly. 

3.  By  obversion,  All  illogical  work  is  unscholarly. 

In  the  final  proposition,  which  is  the  contrapositive,  it 
will  be  seen  that  the  subject  and  predicate  of  the  original 
proposition  have  been  interchanged  and  each  replaced  by 
its  corresponding  contradictory.  The  contrapositive  may  be 
defined,  therefore,  as  a transformation  which  substitutes 
for  the  given  terms  their  corresponding  contradictories, 
and  at  the  same  time  interchanges  the  subject  and  predi- 
cate positions.  The  three  processes  by  which  the  contra- 
positive is  formed  may  be  omitted,  and  the  contrapositive 
formed  directly  according  to  the  above  definition.  The 
processes,  however,  form  the  proof  that  this  direct  transfor- 
mation is  admissible.1 

There  is  another  proof  for  the  contrapositive  of  a uni- 
versal affirmative  which  is  as  follows  : Given,  All  x is  y ; 
then  All  not-y  is  not-x\  For  what  is  not-y  must  be  either 
x or  not-x.  But  if  it  is  x,  it  is  also  y,  according  to  the 
given  proposition.  This,  however,  is  impossible,  for  the  same 
concept  cannot  be  both  not-y  and  y.  Therefore,  the  other 
alternative  must  be  true,  namely,  that  not-y  must  be  not-x, 
which  was  to  be  proved. 

When  an  A proposition  is  given,  its  contrapositive  is  also 
an  A proposition.  When,  however,  the  given  proposition  is 
of  the  E form,  there  is  a loss  of  logical  force,  and  the  result 
of  the  three  processes  is  an  0 proposition. 

1 Some  logicians  regard  the  contrapositive  as  the  result  merely  of  the 
two  processes,  obversion  and  conversion.  This,  however,  is  merely  a mat- 
ter of  definition,  and  no  confusion  can  result,  because  the  additional  process 
of  obversion  simply  carries  the  operation  one  step  farther. 


116 


DEDUCTIVE  LOGIC 


Given,  No  insane  persons  are  responsible,  E. 

(1)  By  obversion,  All  insane  persons  are  irresponsible,  A. 

(2)  By  conversion,  Some  irresponsible  persons  are  in- 
sane, I. 

(3)  By  obversion,  Some  irresponsible  persons  are  not 
sane,  0. 

In  a similar  manner  it  will  be  readily  seen  that  the 
contrapositive  of  an  0 proposition  is  also  an  0 proposition. 
The  I proposition  yields  no  contrapositive,  because  the  first 
step  of  obversion  gives  an  0 proposition ; the  second  step  of 
conversion  cannot  be  applied  to  an  0 proposition,  and  con- 
sequently the  process  is  blocked  at  this  point. 

It  is  well  to  remember  that  the  contrapositive  is  formed 
by  taking  contradictories  of  the  original  subject  and  predi- 
cate ; for,  if  contraries  are  taken,  the  process  is  rendered 
invalid.  For  instance,  if  we  have  given  the  proposition, 
All  honest  acts  are  moral,  the  contrapositive,  according  to 
rule,  would  seem  to  be,  All  immoral  acts  are  dishonest. 
This,  however,  is  not  true,  and  the  reason  is  that  the  terms 
“honest”  and  “dishonest”  are  not  contradictory  but  contrary, 
for  between  honest  and  dishonest  acts  there  is  the  middle 
ground  corresponding  to  acts  concerning  which  the  ques- 
tion of  honesty  is  not  raised  at  all. 


CHAPTER  XIV 


A GENERALIZATION  OF  IMMEDIATE  INFERENCES 

As  the  various  immediate  inferences  by  opposition  have 
been  generalized  in  the  ancient  logical  square,  the  question 
suggests  itself,  cannot  a similar  method  be  applied  to  the 
other  forms  of  immediate  inference  ? And  the  following 
is  the  result  of  the  problem  thus  proposed. 

The  possible  ti’ansformations  of  a simple  proposition  may 
occur  in  any  of  the  following  ways : by  a change  of  the 
quality  of  a proposition,  i.e.  change  from  affirmative  to 
negative  and  vice  versa;  or,  by  a change  of  quantity,  i.e. 
from  universal  to  particular  and  vice  versa;  or  by  a change 
of  either  subject  or  predicate  terms  by  substituting  for  them 
their  respective  contradictory  terms ; or,  by  an  interchange 
of  subject  and  predicate  in  the  proposition.  Of  these  pro- 
cesses or  combinations  of  them,  the  ones  which  are  legiti- 
mate inferences  are  as  follows:  — 

Having  given,  for  example,  an  A proposition,  All  x is  y, 
it  is  possible  to  infer : — 

(1)  The  converse,  Some  y is  x. 

(2)  The  obverse,  No  x is  not-,?/. 

(3)  Converted  obverse,  No  not-y  is  x. 

(4)  Contrapositive,  All  not-y  is  not-x. 

(5)  Obverted  converse,  Some  y is  not  not-x. 

(6)  Inverse,  Some  not-x  is  not  y.1 

(7)  Obverted  inverse,  Some  not-x  is  not-y. 

1 The  inverse  of  a proposition  has  the  same  predicate,  but  for  its  sub- 
ject the  contradictory  of  the  original  subject. 

117 


118 


DEDUCTIVE  LOGIC 


These  transformations  may  be  comprehended  in  the  fol- 
lowing logical  square : — 

x E not-y 


A or  I A or  I 


y 0 not-x 

Here  I have  placed  the  terms  *,  y,  and  their  contradic- 
tions, not-*,  not-y,  in  the  corners  of  the  square  so  that  any 
term  and  its  contradiction  will  be  situated  diagonally  oppo- 
site. The  letter  A,  E,  I,  or  O,  indicates  that  the  two  terms 
between  which  the  letter  is  situated  may  be  formed  into  a 
proposition  of  the  character  represented  by  that  letter,  and 
in  every  case  such  a proposition  is  a legitimate  inference 
from  the  original  proposition,  All  * is  y.  Thus,  between 
the  two  upper  terms,  * and  not-y,  there  are  possible  two 
universal  negative  propositions,  one  the  converse  of  the 
other : — 

No  * is  not-y,  E. 

No  not-y  is  *,  E. 

Between  the  two  lower  terms,  two  particular  negative 
propositions : — 

Some  y is  not  not-*,  0. 

Some  not-*  is  not  y,  0. 

Between  either  upper  one  as  subject  and  corresponding 
lower  one  as  predicate  there  is  possible  a universal  affirma- 
tive. This  gives : — 

All  * is  y,  A. 

All  not-y  is  not-*,  A. 

Between  either  lower  term  and  corresponding  upper  one 
there  is  possible  a particular  affirmative.  This  gives : — 


A GENERALIZATION  OF  IMMEDIATE  INFERENCES  110 


Some  y is  x,  I. 

Some  not-x  is  not -y,  I. 


By  comparison  of  these  results  with  the  legitimate  infer- 
ences given  at  the  beginning  of  this  discussion,  there  will 
be  seen  an  exact  correspondence.  This  square,  therefore, 
summarizes  exhaustively  all  possible  legitimate  infer- 
ences. 

I would  note  in  passing  that  of  the  two  inferences  of  the 
0 form,  while  one  is  the  converse  of  the  other,  still  it  is 
not  derived  from  the  other  by  conversion,  which  process 
is  logically  inadmissible,  but  is  derived  independently : 
Some  y is  not  not-x,  being  the  obverted  converse,  and  Some 
not-x  is  not  y being  the  inverse. 

Again,  when  E is  the  original  proposition,  the  possible 
inferences  are : — 


(1)  No  y is  x. 

(2)  All  x is  not-y. 

(3)  All  y is  not-x. 

(4)  Some  not-y  is  x. 

(5)  Some  not-y  is  not  not-x. 

(6)  Some  not-x  is  y. 

(7)  Some  not-x  is  not  not-y. 


All  of  these  are  comprehended  in  the  same  square  as  that 
indicating  the  inferences  from  an  A proposition,  provided 
the  positions  of  y and  not-y  are  interchanged.  This  gives 
the  following  square  for  inferences  from  an  A1  proposition : — 


x 


E y 


A or  I 


A or 


not-y  o 


not-x 


120 


DEDUCTIVE  LOGIC 


This  agrees  with  the  fact  that  an  A proposition,  All  x is 
y,  becomes  by  obversion  an  E proposition,  No  x is  not-y; 
in  this  transformation  it  is  observed  that  not-?/  has  displaced 
y.  Such  a substitution  will  affect  all  inferences  from  the 
original  proposition  uniformly.  With  this  one  change, 
therefore,  the  inferences  exhibited  by  the  A square  and 
the  E square  coincide  throughout. 

The  I square  is  the  same  as  the  A square,  with  the 
exceptions  that  the  E and  A inferences  become  0 and  I, 
respectively,  and  that  the  propositions  indicated  by  the  two 
horizontal  lines  of  the  square  are  to  be  formed  by  reading  from 
left  to  right  only ; also  that  no  inference  is  possible  between 
not-x  and  not-//,  i.e.  no  contrapositive  of  an  I proposition  is 
possible.  The  I square  is  as  follows : — 

x 0 noUy 


1 


y 0 not-x 

The  possible  inferences  based  upon  an  I proposition  are 
indicated  in  this  square,  and  are  as  follows : — 

(1)  Some  y is  x. 

(2)  Some  x is  not  not-y. 

(3)  Some  y is  not  not-x. 

The  0 square  is  the  same  as  the  I square,  provided  y and 
not,-?/  are  interchanged  as  above  in  the  case  of  the  E and  A 
diagrams.  The  following  is  the  0 square:  — 

x 0 y 


I 


not-y  0 not-X 


A GENERALIZATION  OF  IMMEDIATE  INFERENCES  121 


The  possible  inferences  based  upon  an  0 proposition  are 
indicated  in  this  square,  and  are  as  follows  : — 

(1)  Some  x is  not -y. 

(2)  Some  not-?/  is  x. 

(3)  Some  not -y  is  not  not-*. 

There  is  no  relation  between  y and  not-*  as  a possible  form 
of  inference,  inasmuch  as  the  inverse  of  an  0 proposition  is 
impossible. 


CHAPTER  XV 


MEDIATE  INFERENCE  — THE  SYLLOGISM 

True  inference  always  contains  an  element  of  mediation. 
It  is  the  process  of  grounding  a judgment  upon  some  other 
judgment  essentially  related  to  it,  and  which  stands  as  the 
warrant  of  its  truth.  The  reference  of  a judgment  to  an- 
other judgment  as  its  ground  implies  a knowledge  of  a 
third  judgment  which  expresses  a universal  and  necessary 
connection  between  the  two.  The  complete  process  of  me- 
diate inference,  therefore,  consists  in  exhibiting  a judgment 
as  the  necessary  result  of  the  combination  of  two  other 
judgments.  Thus,  the  judgment  that  a certain  heap  of 
black  sand  is  magnetic  is  justified  when  referred  to  its 
ground,  namely,  that  it  attracts  iron  filings.  To  complete 
the  process,  however,  a third  judgment  is  necessary,  which 
shall  express  the  constant  bond  of  connection  between  the 
given  judgment  and  its  alleged  ground,  such  as  the  judg- 
ment that  whatever  attracts  iron  is  magnetic. 

This  form  which  mediate  inference  naturally  takes  is  the 
syllogism,  which  is  a process  of  combining  two  judgments  so 
as  to  produce  a third.  The  above  judgments  expressed  in 
syllogistic  form  would  be : — 

Whatever  attracts  iron  is  a magnet. 

This  black  sand  attracts  iron. 

This  black  sand  is  a magnet. 

It  will  be  observed  that  the  two  judgments  which  combine 
to  produce  the  third  have  a term  in  common.  This  is  the 
middle  term  of  the  syllogism.  Moreover,  the  third  judg- 
ment is  formed  by  eliminating  the  middle  term  and  taking 

122 


MEDIATE  INFERENCE 


123 


as  its  subject  and  predicate  respectively  the  remaining 
term  in  each  of  the  two  given  judgments.  The  subject  of 
the  judgment  thus  formed  is  called  the  minor  term  of  the 
syllogism,  and  the  predicate  the  major  term.  Minor  and 
major  are  applied  to  these  terms  because  in  any  judgment 
the  predicate  generally  refers  to  a larger  class  than  the 
subject. 

Of  the  two  given  judgments,  the  one  containing  the  major 
term  is  called  the  major  premise;  and  the  one  containing 
the  minor  term,  the  minor  premise.  The  premises  take 
their  names  from  the  major  and  minor  terms,  and  not  the 
terms  from  the  premises.  In  most  syllogisms,  the  major 
premise  is  placed  before  the  minor;  but  this  order  is  not 
essential  to  the  structure  of  the  syllogism,  or  is  it  by  any 
means  an  invariable  practice.  The  judgment  which  is 
derived  from  the  combination  of  the  two  premises  is  called 
the  conclusion. 

It  is  the  peculiar  function  of  the  major  premise  to  ex- 
hibit some  phase  of  our  general  knowledge;  and  of  the 
minor  premise,  to  exhibit  some  more  particular  phase  of 
our  general  knowledge,  or,  as  it  more  frequently  occurs, 
some  special  case  embodied  in  a concrete  experience.  It 
is  the  function,  therefore,  of  the  two  combined,  — that  is,  of 
the  syllogism  itself,  — to  apply  universal  knowledge  to  a spe- 
cial case  so  as  to  yield  its  true  interpretation.  The  process 
is  one  which  consists  essentially  in  eliminating  the  middle 
or  common  term.  It  is  the  same  process  which  we  find  in 
algebra.  Equations  are  merely  a special  case  of  judgment. 
The  following  is  in  every  respect  a true  syllogism : — 

x = y. 

y = z. 

x = z. 

There  is,  however,  a difference  between  the  algebraical 
equation  and  the  ordinary  logical  proposition  in  this  re- 
spect that  in  the  equation  it  is  a matter  of  indifference 


124 


DEDUCTIVE  LOGIC 


whether  we  say  a;  = y or  y = x ; but  the  proposition  cannot 
be  converted  in  this  manner  without  impairing  its  logical 
significance. 

Compare  the  following  syllogisms  : — 

(1)  All  x is  y.  (2)  All  y is  a:.  (3)  Some  x is  y. 

All  z is  x.  All  z is  x.  All  z is  a;. 

.\  All  z is  y.  All  z is  y.  All  z is  y. 

It  is  obvious  that  the  first  of  these  syllogisms  is  valid,  the 
other  two  invalid.  Moreover,  it  is  evident  that  the  position 
of  the  terms  in  the  syllogism,  as  well  as  the  kind  of  proposi- 
tions employed  in  its  structure,  whether  A,  E,  I,  or  O, 
have  an  essential  bearing  upon  its  validity.  How  this 
comes  to  pass  and  what  criteria  may  be  formulated  for 
testing  the  validity  of  syllogisms  will  appear  in  the  fol- 
lowing exposition  concerning  the  so-called  distribution  of 
terms. 

A term  is  said  to  be  distributed  when  it  is  used  in  a uni- 
versal sense,  and  undistributed  when  it  is  used  in  a limited 
or  partial  sense.  The  word  distributed  is  regarded  as 
synonymous  with  universal,  because  it  is  of  the  nature  of  a 
universal  to  distribute  or  apply  the  full  force  of  its  signifi- 
cance to  every  individual  case  which  is  subsumed  under  it. 
In  the  proposition,  All  the  schoolmen  were  logicians,  the 
subject  is  distributed  in  the  connection  in  which  it  is  used, 
so  that  what  is  affirmed  of  the  class  that  they  were  logicians 
can  be  affirmed  of  every  individual  of  the  class.  The  term 
logicians  in  this  connection  is  undistributed,  because  it  is 
only  a part  of  the  class  of  logicians  that  can  be  identified 
with  the  schoolmen. 

In  respect  to  the  four  propositions,  A,  E,  I,  0,  the  follow- 
ing are  the  possibilities  as  regards  distributed  and  undistrib- 
uted terms. 

1.  The  universal  affirmative  distributes  the  subject  but 
not  the  predicate.  This  will  be  evident,  if  the  given  propo- 


MEDIATE  INFERENCE 


125 


sition  be  converted,  for  while  All  x is  y,  by  conversion 
Some  y is  x. 

x is  seen  to  be  distributed,  and  y undistributed. 

2.  The  universal  negative  distributes  both  subject  and 
predicate.  It  is  a matter  of  indifference  whether  we  say  Ho 
x is  y,  or  by  conversion  No  y is  x.  In  the  one  case  x is  wholly 
excluded  from  y,  but  that  is  the  same  as  excluding  y wholly 
from  x. 

x is  distributed,  and  y is  distributed. 

3.  The  particular  affirmative  does  not  distribute  either 
term.  For  Some  * is  y gives  by  conversion  Some  y is  x. 

.*.  x is  undistributed  and  y is  undistributed. 

4.  The  particular  negative  does  not  distribute  the  sub- 
ject but  does  distribute  the  predicate.  This  cannot  be 
shown  by  converting  the  given  proposition,  for  the  par- 
ticular negative  does  not  admit  of  simple  conversion.  How- 
ever, given  the  proposition  Some  x is  not  y,  it  is  evident 
that  the  subject,  some  x,  is  excluded  wholly  from  y,  there- 
fore such  exclusion  must  cut  off  all  of  y from  that  special 
some  x,  which  is  its  subject. 

.-.  x is  undistributed  but  y is  distributed. 

The  above  results  may  be  tabulated  as  follows,  the  dis- 
tributed terms  being  marked  with  a V and  the  undistributed 
with  a °. 

✓ . ° 

All  x is  y A. 

</  v/ 

No  x is  y E. 

o . o 

Some  x is  y I. 

o # V/ 

Some  x is  not  y 0. 

In  determining  whether  a term  is  distributed  in  any 
given  proposition,  the  distribution  of  the  subjects  will  be 
readily  recognized  because  indicated  by  the  qualifying  terms, 


126 


DEDUCTIVE  LOGIC 


“all,”  “some,”  “none,”  or  “some  not.”  The  distribution 
of  the  predicates  may  be  recalled  by  the  following  gen- 
eralization which  is  obvious  upon  inspection  of  the  above 
table. 

Affirmative  propositions  do  not  distribute  their  predi- 
cates. 

Negative  propositions  do  distribute  their  predicates. 

In  reference  to  the  criticism  of  any  syllogism,  there 
are  two  fundamental  rules  of  distribution  which  must  be 
observed : — 

1.  The  middle  term  must  be  distributed  at  least  once. 

2.  If  a term  is  distributed  in  the  conclusion,  it  must  also 
be  distributed  in  its  premise. 

The  middle  term  must  be  distributed  at  least  once  in 
order  to  provide  a common  point  of  connection  between  the 
two  premises.  For  if  the  middle  term  is  undistributed  in 
both  premises,  then  the  major  term  is  related  to  a part  of 
the  middle  term  in  the  major  premise,  and  the  minor  term 
is  related  to  a part  of  the  middle  term  in  the  minor  premise, 
and  there  is  no  assurance  whatever  that  these  two  parts 
have  anything  in  common. 

Given  the  premises  (1)  All  x is  y, 

(2)  All  z is  y, 

the  following  diagrams  will  represent  these  relations 
respectively. 


MEDIATE  INFERENCE 


127 


There  is  nothing  in  the  above  relations, 
however,  to  indicate  whether  within  the 
common  circle  y,  x and  2 be  wholly  apart 
as  in  the  following  diagram 


or  whether  they  have  some  common 
ground  as 


or  whether  x falls  within  z as 


or  whether  z falls  within  x as 


The  relation  between  x and  z is  left  wholly  indeterminate 
by  the  given  premises.  If,  however,  the  middle  term  is  dis- 
tributed at  least  once,  it  serves  to  bring  the  two  premises 
into  a logically  significant  relation  freed  from  all  ambiguity. 
It  is  not  necessary,  however,  that  it  should  be  distributed 
twice ; for  the  object  of  its  distribution  is  to  connect  the 
two  premises.  This  connection  once  effected,  it  is  not  neces- 


128 


DEDUCTIVE  LOGIC 


sary  to  secure  it  again ; if  the  middle  term  should  happen 
to  be  distributed  in  both  premises,  the  existing  connection 
is  merely  confirmed  and  in  no  sense  invalidated  by  such 
twofold  distribution. 

The  following  syllogism  will  serve  as  a concrete  illustra- 
tion of  the  fallacy  of  an  undistributed  middle : — 

All  agnostics  repudiate  the  methods  of  metaphysical  in- 
quiry. 

All  materialists  repudiate  the  methods  of  metaphysical 
inquiry. 

All  agnostics  are  materialists. 

This  conclusion  does  not  necessarily  follow.  The  middle 
term,  being  in  the  predicate  of  an  affirmative  proposition  in 
each  case,  is  undistributed. 

The  second  rule  that  a term  distributed  in  the  conclusion 
must  also  be  distributed  in  its  premise,  is  directed  against 
that  illogical  procedure  from  a term  used  in  a partial  sense 
to  the  same  term  used  in  the  universal  sense.  In  the  dis- 
cussion concerning  the  opposition  of  propositions,  it  was 
seen  that  the  truth  of  the  particular  does  not  imply  the 
truth  of  the  universal.  It  is  the  same  principle  which 
emerges  here.  The  truth  of  the  universal  carries  with  it, 
however,  the  truth  of  the  particular;  therefore,  it  is  per- 
missible to  have  a term  distributed  in  the  premise  and 
undistributed  in  the  conclusion.  The  beginner  in  logic  is 
liable  to  confuse  these  two  modes  of  procedure ; therefore  it 
should  be  especially  held  in  mind  that  the  invalid  procedure 
is  only  from  a term  undistributed  in  the  premise  to  the  same 
term  distributed  in  the  conclusion,  or  from  the  particular 
to  the  universal.  As  a concrete  illustration,  take  the  fol- 
lowing syllogism  in  which  the  distribution  of  terms  is 
marked : — 

V ' O 

All  foreigners  who  are  naturalized  may  vote. 

v V 

No  native-born  citizens  are  foreigners  who  are  naturalized. 

v v 

No  native-born  citizens  may  vote. 


MEDIATE  INFEKENCE 


129 


This  conclusion  is  obviously  incorrect;  the  major  term 
is  distributed  in  the  conclusion  and  undistributed  in  the 
premise.  When  such  invalid  procedure  is  concerned  with 
the  major  term,  it  is  called  the  illicit  process  of  the  major 
term,  or  simply  illicit  major;  when  it  is  concerned  with  the 
minor  term,  it  is  the  illicit  process  of  the  minor  term,  or 
illicit  minor. 

There  are  several  special  cases  in  which  the  general  rules 
for  distribution  must  be  somewhat  modified : — 

1.  The  predicate  of  some  affirmative  propositions  is  dis- 
tributed because  of  a special  significance  which  it  may 
possess.  While  according  to  form  alone  it  would  be  undis- 
tributed, the  sense  may  afford  additional  information  which 
justifies  its  distribution.  This  is  the  same  principle  which 
was  seen  to  operate  in  reference  to  the  conversion  of  a 
universal  affirmative  proposition,  All  x is  y to  All  y is  x 
when  x and  y are  coextensive  terms. 

Thus  the  following  syllogism  is  invalid  because  of  an 
undistributed  middle : — 

All  x is  y. 

All  z is  y. 

.-.  All  z is  x. 

Here  the  form  alone  serves  as  the  test  of  its  validity. 
But  in  the  filling  up  of  such  a form  with  significant  terms, 
the  meaning  may  possibly  render  such  a syllogism  valid. 
Thus, 

Every  government  by  the  people  is  a democracy. 

The  United  States  is  a democracy. 

.-.The  United  States  is  a government  by  the  people. 

The  middle  term  in  this  syllogism  is  undistributed  as 
regards  its  bare  form.  As  regards  the  meaning  of  the  terms 
the  major  premise  may  be  converted  simply,  every  democ- 
racy is  a government  by  the  people.  The  term  democracy  is 
in  reality  therefore  distributed,  the  subject  and  predicate 
terms  of  the  major  premise  being  coextensive. 


130 


DEDUCTIVE  LOGIC 


2.  There  are  certain  qualifying  words  which,  while  restrict- 
ing the  subject  at  the  same  time,  distribute  the  predicate. 
In  all  propositions  of  this  kind  the  subject  is  undistributed, 
and  the  predicate  is  distributed.  The  qualifying  words  are 
“only,”  “none  but,”  “alone,”  and  the  like.  In  the  proposi- 
tion, None  but  members  of  the  union  will  be  employed,  the 
subject  is  undistributed,  and  the  predicate  distributed ; the 
logical  force  of  this  proposition  will  be  the  more  readily 
seen  if  we  convert  it.  It  then  becomes,  All  who  are  em- 
ployed must  be  members  of  the  union;  in  this  form,  the 
subject  is  distributed,  the  predicate  undistributed,  as  it  is  a 
universal  affirmative. 

In  the  two  syllogisms  following,  the  first  is  valid,  the 
second  is  invalid,  being  a case  of  undistributed  middle : — 

(1)  None  but  members  of  the  union  will  be  employed. 

A certain  man  was  employed. 

He  must  have  been  a member  of  the  union. 

(2)  None  but  members  of  the  union  will  be  employed. 

A certain  man  is  a member  of  the  union. 

•\  He  must  be  employed. 

In  the  criticism  of  the  various  modes  of  reasoning  atten- 
tion should  be  drawn  to  the  fact  that  we  seldom  find  our 
thought  expressed  in  the  form  of  a complete  syllogism. 
Usually  one  of  the  parts  of  the  syllogism  is  omitted,  not, 
however,  because  its  force  is  unessential  to  the  reasoning 
process,  but  because  it  is  so  obvious  that  it  is  unnecessary  to 
state  it  explicitly.  This  condensed  form  of  the  syllogism  is 
known  as  the  Enthymeme,  so  called,  as  its  name  indicates, 
because  a part  of  the  syllogism  is  not  expressed  but  in  the 
reasoning  process  is  carried  along  in  the  mind.  The  omitted 
portion  is  usually  the  major  premise ; that  is,  the  general 
principle  of  which  the  course  of  the  reasoning  in  question 
forms  the  special  case.  Both  the  minor  premise,  or  the 
conclusion,  may  also  be  omitted  in  the  construction  of  an 
enthymeme.  There  are  three  kinds  of  enthymeme : — 


MEDIATE  INFERENCE 


131 


1.  With  the  major  premise  omitted. 

This  enterprise  will  tend  to  increase  the  public  wealth, 
because  it  will  promote  the  general  happiness  of  the  people. 

2.  With  minor  premise  omitted. 

That  expedition  is  doomed  to  failure,  because  no  small 
body  of  men  insufficiently  equipped  and  cut  off  from  their 
base  of  supplies  can  ever  reduce  so  strongly  fortified  a 
garrison. 

3.  With  conclusion  omitted. 

All  members  of  that  conference  were  traitors  to  their 
party.  And  you  were  a member  of  that  conference.  Noth- 
ing more  need  be  said. 

The  enthymeme  may  be  tested  as  regards  its  validity  by 
supplying  the  omitted  part,  and  then  applying  the  usual 
rules  of  the  syllogism.  But,  inasmuch  as  the  enthymeme 
expresses  the  immediate  connection  between  two  judgments, 
it  may  be  subjected  to  direct  criticism  according  to  the 
following  criteria : — 

If  the  major  premise  is  omitted,  the  enthymeme  consists 
of  a special  case  referred  to  its  ground,  This  is  x because 
it  is  y.  The  enthymeme  is  valid,  provided  the  ground  as- 
signed for  the  special  case  applies  as  well  to  all  other  cases 
of  the  same  kind ; that  is,  according  to  the  symbols  used, 
if  All  y is  x. 

In  the  enthymeme,  He  is  a free-trader  because  he  is  a 
democrat,  the  connection  is  a valid  one  provided  all  demo- 
crats are  free-traders. 

Again,  if  the  enthymeme  has  the  minor  premise  omitted, 
it  may  be  expressed  in  symbols,  as  follows:  — 

A certain  thing  is  x,  because  All  z is  x.  In  such  a relation, 
the  special  case  must  be  recognized  as  a special  case  of  the 
universal ; that  is,  we  must  know  that  the  thing  in  question 
is  z. 

For  instance,  given  the  enthymeme  as  follows : That 
man  is  a German,  for  all  the  crew  are  Germans.  The 
inference  based  upon  the  assigned  ground  is  valid,  provided 


132 


DEDUCTIVE  LOGIC 


we  know  that  the  man  in  question  is  a member  of  the  crew ; 
that  is,  if  the  single  case  falls  with  the  area  of  the  universal 
which  is  stated  as  its  ground. 

Syllogisms  may  be  combined  in  various  ways  into  chains 
of  reasoning.  When  the  conclusion  of  one  syllogism  becomes 
the  premise  of  a second  syllogism,  the  former  is  called  the 
prosyllogism  and  the  latter  the  episyllogism.  When  we 
combine  a number  of  prosyllogisms  and  episyllogisms  so 
that  all  the  conclusions  except  the  last  are  omitted,  the 
chain  of  reasoning  is  called  the  Sorites.  There  are  two 
forms  of  the  Sorites,  known  as  the  Aristotelian  and  the 
Goclenian.1 

These  forms  may  be  expressed  symbolically  as  follows : — 


I 

Aristotelian  Sorites 

A is  B. 

B is  a 
<7  is  D. 

D is  E. 

A is  E. 


II 

Goclenian  Sorites 

D is  E. 

C is  D. 

B is  a 
A is  B. 

A is  E. 


It  will  be  seen  that  the  middle  terms  cancel  through- 
out, and  the  conclusion  is  formed  from  the  remaining  terms 
in  the  first  and  last  premises.  Thus,  it  may  be  reasoned 
that  a certain  political  boss  has  caused  his  chosen  man  to  be 
made  governor  of  New  York  ; for  he  controls  the  machine, 
and  the  machine  controls  the  party,  and  the  party  controls 
the  state  vote,  and  the  state  vote  creates  the  governor.  The 
Sorites  is  commonly  used  to  indicate  the  various  links  of 
cause  and  effect  which  may  be  interpolated  between  an 
effect  and  a remote  cause. 

The  Sorites  often  appears  in  hypothetical  form,  for  the 
reason  that  the  causal  relation  is  best  expressed  by  a 
hypothetical.  In  the  life  of  Sir  James  Fitzjames  Stephen, 

1 Named  from  Goclenius,  a German  logician  of  the  sixteenth  century. 


MEDIATE  INFERENCE 


133 


the  following  remark  of  his  tutor  appears,  which  illustrates 
the  hypothetical  form  of  the  Sorites,  and  at  the  same  time 
will  serve  to  show  how  plausibly  a Sorites  may  express  a 
subtle  fallacy : “ If  you  do  not  take  more  pains,  how  can  you 
ever  expect  to  write  good  longs  and  shorts  ? If  you  do  not 
write  good  longs  and  shorts,  how  can  you  ever  be  a man 
of  taste  ? If  you  are  not  a man  of  taste,  how  can  you  ever 
hope  to  be  of  use  in  the  world  ? ” 


CHAPTER  XVI 


MOOD  AND  FIGUKE 

A syllogism  may  be  constructed  by  combining  in  various 
ways  the  four  propositions,  A,  E,  I,  and  0.  The  particular 
combination  employed  in  any  one  syllogism  constitutes  the 
mood  of  that  syllogism.  Thus,  to  refer  to  a syllogism  as  hav- 
ing the  mood  AAA,  means  that  the  premises  and  conclusion 
are  all  universal  affirmative  propositions;  the  mood  EAE 
means  that  the  major  premise  is  a universal  negative,  the 
minor  premise  a universal  affirmative,  and  the  conclusion  a 
universal  negative.  The  three  letters  designating  the  mood 
are  to  be  interpreted  in  the  order  of  major  premise,  minor 
premise,  and  conclusion. 

The  problem  which  the  subject  of  mood  presents  is  to 
find  which  moods  are  valid ; for  there  are  sixty-four  possi- 
ble permutations  of  three  propositions  out  of  four,  repeti- 
tions such  as  AAA  being  allowed.  In  order  to  discriminate 
between  the  valid  and  invalid  moods,  the  following  rules 
must  be  taken  to  guide  us : — 

1.  A particular  premise  gives  a particular  conclusion. 

2.  Two  particular  premises  give  no  conclusion. 

3.  A negative  premise  gives  a negative  conclusion,  and 
conversely  if  the  conclusion  is  negative,  one  of  the  premises 
must  be  negative. 

4.  Two  negative  premises  give  no  conclusion. 

The  first  and  second  rules  follow  from  the  rules  relating 
to  distribution  of  terms ; this  is  obvious  upon  simple  inspec- 
tion. The  third  rule  as  to  a negative  premise  giving  a nega- 
tive conclusion  and  its  converse  is  based  upon  the  necessary 

134 


MOOD  AND  FIGURE 


135 


relation  that  if  one  of  the  two  terms  major  or  minor  agrees 
with  the  middle  term  and  the  other  disagrees,  then  they 
must  necessarily  disagree  with  each  other ; that  is,  the  con- 
clusion expressing  this  disagreement  must  be  in  the  negative 
form.  As  to  the  rule  that  two  negatives  give  no  conclusion, 
it  is  evident  that  when  the  major  and  minor  terms  both  are 
excluded  from  all  relation  to  the  middle  term,  no  indication 
whatever  is  given  as  to  their  relation  to  each  other.  Ac- 
cepting these  rules  therefore  as  binding,  let  us  examine  their 
effect  upon  the  sixty -four  possible  permutations.  This  prob- 
lem we  will  divide  into  two  parts : — 

(1)  What  pairs  of  premises  are  valid? 

(2)  What  valid  conclusions  follow  from  them  ? 

First,  the  major  premise  may  be  either  A,  E,  I,  or  0,  and 
the  minor  premise  may  be  either  A,  E,  I,  or  0.  The  per- 
mutations resulting  from  combining  these  letters  to  form 
possible  pairs  of  premises  are  as  follows : — 

AA,  AE,  AI,  AO. 

EA,  EE,  El,  EO. 

I A,  IE,  II,  10. 

OA,  OE,  01,  00. 

Of  these  the  following  cannot  stand  as  pairs  of  prem- 
ises : — 

EE,  because  there  are  two  negatives. 

EO,  because  there  are  two  negatives. 

II,  because  there  are  two  particulars. 

10,  because  there  are  two  particulars. 

01,  because  there  are  two  particulars. 

OE,  because  there  are  two  negatives. 

00,  because  there  are  two  negatives,  and  also  two  par- 
ticulars. 

Eliminating  these  tentative  forms,  there  remain  the  fol- 
lowing : — 


136 


DEDUCTIVE  LOGIC 


AA,  AE,  AI,  AO. 

EA,  EI. 

I A,  IE. 

OA. 

The  second  question  is,  given  the  above  premises,  what 
conclusions  are  possible  ? 

AA  will  give  as  a conclusion  either  i or  7;  but  will  not 
give  E or  0,  for  a negative  conclusion  requires  one  of  the 
premises  to  be  negative.  By  inspection,  after  the  same 
manner,  it  will  be  found  that  AE  will  give  two  conclusions, 
E and  0 ; so  also  EA.  The  remaining,  with  the  exception 
of  IE,  have  each  one  conclusion,  — All,  AOO,  EIO,  IAI, 
OAO. 

The  premises  IE  would  seem  to  require  the  conclusion  0 
and  so  form  a valid  mood  IEO.  This  mood,  in  fact,  squares 
with  all  the  special  rules  which  we  have  formed  above  to 
guide  us  in  discussing  this  present  problem.  However,  it  is 
impossible  to  construct  a syllogism  in  this  form  which  does 
not  contain  an  illicit  major,  for  the  conclusion,  being  nega- 
tive, distributes  the  major  term,  and  the  major  premise,  being 
7,  cannot  distribute  either  subject  or  predicate  term.  For 
example,  take  the  following  syllogism  : — 

Some  x is  y I. 

No  z is  x E. 

Some  z is  not  y 0. 

7 is  here  distributed  in  the  conclusion,  but  not  in  the 
premise.  The  syllogism,  therefore,  in  this  form  is  impossible. 

The  valid  moods  which  remain  after  this  process  of  elimi- 
nation which  we  have  now  completed  are  as  follows:  — 

AAA  AEE  EAE  All  EIO  OAO 

(AAI)  ( AEO ) (EAO)  AOO  IAI 

The  three  in  parentheses  are  called  the  weak  moods  of 
the  syllogism,  because  the  conclusion  in  each  case  is  really 


MOOD  AND  EIGUKE 


137 


implied  in  the  stronger  conclusion  immediately  above  it,  and 
therefore  they  do  not  constitute  distinct  types.  The  truth 
of  A always  necessitates  the  truth  of  7,  and  the  truth  of  E 
always  necessitates  the  truth  of  O. 

There  remain  all  together  only  eight  distinct  types  out 
of  the  sixty-four  which  are  valid  forms  of  the  syllogism. 

There  is  still  a further  problem  which  remains  to  be 
considered,  whether  all  of  these  moods  are  valid  irrespec- 
tive of  the  relative  positions  of  the  major,  minor,  and  mid- 
dle terms  in  the  syllogism.  The  position  of  the  middle 
term  in  reference  to  the  major  and  minor  term  constitutes 
what  is  known  as  the  figure  of  the  syllogism.  If  we 
represent  the  middle  term  by  31,  the  minor  term  by  S,  and 
the  major  term  by  P,  the  four  possible  figures  are  as 
follows : — 


I 


II  III  IV 


M.  P.  P.  3f.  31.  P.  P.  3f. 

S.  31.  S.  3f.  31.  S.  31.  S. 

S.  P.  .-.  S.  P.  .-.  S.  P.  .-.  S.  P. 

A change  in  the  relative  position  of  the  terms  will  of 
course  affect  the  matter  of  their  distribution,  and  therefore 
the  validity  of  the  various  moods  in  the  different  figures 
will  turn  upon  the  question  of  the  distribution  of  terms. 
The  two  rules  for  distribution,  it  will  be  remembered,  are 
as  follows : — 


(1)  The  middle  term  must  be  distributed  at  least  once. 

(2)  If  a term  is  distributed  in  the  conclusion,  it  must  be 
distributed  also  in  the  premise. 

The  following  are  the  valid  moods  in  the  several  figures, 
the  invalid  moods  being  stricken  out,  and  the  number 
appended  being  the  number  of  the  rule  violated  in  each 
case : — 


138 


DEDUCTIVE  LOGIC 


Figure  I 

Figure  II 

Figure  III 

Figure  IV 

AAA 

AAA 

-AAA1  (. AAI ) 

-AAA2  (AAI) 

AEE2 

AEE 

-AEE2 

AEE 

EAE 

EAE 

MAE2  (EAO) 

MAE2  (EAO) 

All 

AH1 

All 

-AH1 

-AAO1 

AGO 

-ADD2 

-ADO1 

EIO 

EIO 

EIO 

EIO 

JAf1 

AAA' 

IAI 

IAI 

OAO 

-OAA)2 

OAO 

-OAO2 

The  first  figure  is  called  by  Aristotle  the  perfect  figure, 
for  it  alone,  he  averred,  conforms  to  the  fundamental  canon 
of  all  reasoning.  This  canon  of  Aristotle  is  called  the 
Dictum  de  omni  et  nullo.  It  has  come  down  to  us  from  the 
mediaeval  logicians  and  is  formulated  as  follows  : — 

Whatever  is  predicated  affirmatively  or  negatively  of  a 
whole  class  must  be  predicated  affirmatively  or  negatively 
of  everything  contained  under  that  class.  The  affirmative 
predication  is  expressed  by  the  phrase  de  omni,  and  the 
negative  by  de  nullo.1 

Thus  the  perfect  syllogism  is  a process  of  applying 
our  general  knowledge  (the  major  premise)  to  a special 
case  (minor  premise),  the  conclusion  being  the  special  case 
interpreted  in  the  light  of  our  general  knowledge. 

It  will  be  readily  seen,  also,  upon  inspection,  that  the  first 
figure  is  the  only  one  of  the  four  which  proves  any  one  of 
the  four  propositions,  A,  E,  I,  or  0,  as  its  conclusion. 

The  second  figure  proves  only  negative  conclusions.  It 
is  used  in  proving  distinctions  between  things. 

The  third  figure  proves  only  particular  conclusions.  The 
moods  with  an  I conclusion  are  useful  in  proving  a rule 
by  positive  instances ; the  moods  with  an  0 conclusion  in 
proving  exceptions  to  a rule.  It  will  be  noticed  that  in 
the  third  figure  the  strong  moods  AAA  and  EAE  are 

1 Aristotle  stated  it,  Whatever  is  said  of  the  predicate  is  said  of  the 

subject. 


MOOD  AND  FIGURE 


139 


invalid,  but  the  weakened  mood  AAI  and  EAO  are 
valid. 

The  fourth  figure  was  regarded  by  Aristotle  as  merely 
an  awkward  variety  of  the  figure,  and  therefore  he  ignored 
it  altogether.  His  pupils,  Theophrastus  and  Eudemus, 
however,  added  its  five  moods  to  Figure  I,  calling  them 
indirect  moods.  The  fourth  figure  is  called  the  Galenian 
figure  from  Claudus  Galenus  (died  about  200  a.d.),  who 
insisted  upon  ranking  it  upon  the  same  footing  as  the  other 
three  figures.  In  the  fourth  figure,  also,  the  weakened 
moods  take  the  place  of  their  corresponding  stronger 
moods,  the  latter  being  invalid. 

The  Latin  schoolmen  in  the  thirteenth  century  invented 
a system  of  mnemonic  verses  for  the  purpose  of  assisting 
the  memory  as  regards  the  valid  moods  in  each  figure. 
While  such  a mechanical  device  is  not  needed  by  the  student 
of  logic,  it  is  given  a place  in  the  text  as  a curious  bit  of 
logical  history.  It  furnishes  also  an  excellent  illustration 
of  the  scholastic  type  of  mind.  The  lines  are : — 

Barbara , Celarent,  Darii,  Ferioque  prioris  ; 0 : 

Cesare,  Camestres,  Festino,  Baroko,  secundae, 

Tertia,  Darapti,  Disamis,  Datisi,  Felapton, 

Bokardo,  Ferison , habet ; quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

The  words  printed  in  italics  are  artificial  words  having  no 
significance  whatsoever.  Each  word  represents  a mood,  its 
three  vowels  indicating  the  propositions  which  it  contains. 
The  words  “ prioris,”  “ secundae,”  etc.,  refer,  of  course,  to  the 
figure  in  each  case.  Thus  Barbara  signifies  AAA  of  the  first 
figure;  Disamis,  IAI  of  the  third  figure.  Some  of  the 
consonants  in  these  words  are  also  significant,  indicating 
the  method  by  which  the  moods  in  any  of  the  three  figures 
may  be  reduced  to  the  form  of  the  first  figure.  Aristotle 
insisted  that  a mood  in  any  other  figure  could  be  tested 
as  regards  its  validity  only  after  it  had  been  changed  so 
as  to  conform  to  the  “ perfect  figure.”  This  process  is 


140 


REDUCTIVE  LOGIC 


called  reduction.  The  significance  of  the  consonants  in 
reference  to  this  process  is  as  follows : — 

In  the  several  words,  s indicates  that  the  proposition  rep- 
resented by  the  preceding  vowel  is  to  be  converted  simply ; 
p indicates  that  the  proposition  represented  by  the  preced- 
ing vowel  is  to  be  converted  per  accidens,  or  by  limitation, 
that  is,  changing  all  to  some ; m ( mutare ) indicates  that 
the  propositions  which  stand  as  the  premises  are  to  be 
transposed;  k means  that  an  indirect  proof  is  necessary 
in  order  to  reduce  the  mood  to  the  first  figure.  Moreover, 
the  initial  consonants  of  the  so-called  imperfect  figures  cor- 
respond with  those  of  the  moods  in  the  first  figure  to  which 
they  can  be  reduced. 

Thus  Darapti  reduces  to  Dcirii : — 

The  mood  expressed  by  Darapti  is  AAI  as  in  the 
following : — 

All  B is  A. 

All  B is  C. 

Some  C is  A. 

The  p in  Darapti  indicates  conversion  of  minor  premise 
per  accidens  ; this  gives  the  mood  All  which  is  the  Darii  of 
the  first  figure : — 

All  B is  A. 

Some  C is  B. 

Some  C is  A. 

So  also  Disamis  becomes  Darii : — 

Given  the  syllogism  in  the  form  of  Disamis : — 

Some  B is  A. 

All  B is  C. 

Some  C is  A. 

Here  the  first  s indicates  a simple  conversion  of  the  major 
premises,  the  m a transposition  of  premises,  and  the  final 


MOOD  AND  FIGURE 


141 


s a simple  conversion  of  the  conclusion,  all  of  which  will 
result  as  follows : — 

All  B is  C. 

Some  A is  B. 

Some  A is  C. 
or  Some  C is  A. 

The  process  of  reduction  has  no  practical  value  whatso- 
ever ; as  a device  to  arrange  the  syllogism  in  proper  form  for 
the  testing  of  its  validity,  it  is  wholly  unnecessary.  Every 
syllogism,  whether  of  the  first  or  of  the  other  figures,  may 
be  tested  quietly  by  the  application  of  the  rules  concerning 
the  distribution  of  terms.  If  the  middle  term  is  distributed, 
and  no  illicit  process  either  of  the  major  or  the  minor  term 
is  involved,  the  syllogism  needs  no  further  justification. 


CHAPTER  XYII 


THE  HYPOTHETICAL  AND  DISJUNCTIVE  SYLLOGISMS 

The  hypothetical  syllogism  is  a syllogism  in  which  the 
major  premise  is  a hypothetical  proposition,  the  minor 
premise  a categorical,  and  the  conclusion  a categorical  propo- 
sition also.  The  hypothetical  proposition  is  of  the  general 
form,  — If  a;  is  y,  then  z is  w.  The  conditional  clause  is 
known  as  the  antecedent,  the  following  clause  the  conse- 
quent. 

Let  us  examine  some  hypothetical  proposition  regarding 
it  as  a major  premise,  and  putting  the  question  as  to  how 
many  syllogisms  may  be  constructed  by  means  of  introduc- 
ing various  minor  premises  in  connection  with  it.  Let  us 
take  the  proposition,  If  the  Japanese  are  to  be  victorious 
in  the  war  with  Russia,  they  must  take  Port  Arthur.  With 
this  proposition  as  a major  premise,  there  are  four  minor 
premises  possible  according  as  we  affirm  or  deny  the  ante- 
cedent, or  affirm  or  deny  the  consequent,  as  follows  : — 

(1)  They  are  victorious. 

(2)  They  are  not  victorious. 

(3)  They  have  taken  Port  Arthur. 

(4)  They  have  not  taken  Port  Arthur. 

It  will  be  observed  that  the  first  and  fourth  statements 
when  taken  in  connection  with  the  major  premise  give 
definite  conclusions. 

When  we  affirm  the  antecedent,  They  are  victorious,  the 
conclusion  follows  necessarily,  They  roust  have  taken  Port 
Arthur. 


142 


THE  HYPOTHETICAL  SYLLOGISM 


148 


Similiarly,  when  we  deny  the  antecedent,  They  have  not 
taken  Port  Arthur,  the  conclusion  follows,  They  are  not 
victorious. 

Granting  the  truth  of  the  major  premise,  these  two  con- 
clusions must  necessarily  follow  from  the  respective  minor 
premises  as  above  stated. 

But  when  we  come  to  the  other  two  cases,  the  denial  of 
the  antecedent,  or  the  affirmation  of  the  consequent,  the  case 
is  very  different.  If  it  is  stated  that  they  are  not  victorious, 
it  does  not  follow  that  they  did  not  take  Port  Arthur,  for 
they  might  take  Port  Arthur  and  yet  fail  of  victory  for 
some  other  reason.  And  so  also,  if  it  is  stated  that  they 
have  taken  Port  Arthur,  it  cannot  be  inferred  that  they 
are  victorious,  for  here  again  some  other  cause  may  have 
operated  to  prevent  victory. 

In  general  therefore  the  denial  of  the  antecedent  or  the 
affirmation  of  the  consequent  leaves  the  conclusion  indeter- 
minate ; for,  as  in  the  special  case  cited  above,  there  may  be 
some  other  antecedent  which  may  give  rise  to  the  conse- 
quent as  well  as  the  particular  antecedent  connected  with 
it  in  the  given  hypothetical  proposition  which  forms  the 
major  premise.  This  possibility  will  always  render  the  infer- 
ence indeterminate.  If  however  it  is  known  that  the 
given  antecedent  is  the  sole  antecedent  of  the  given  conse- 
quent, and  therefore  every  other  possibility  is  eliminated, 
then  the  denial  of  the  antecedent,  or  the  affirmation  of  the 
consequent,  will  also  give  a determinate  conclusion.  This 
special  case  of  the  hypothetical  syllogism  may  be  recognized 
by  the  simple  test  of  conversion.  Thus  if  the  hypothetical 
major  premise  can  be  converted  simply,  then  any  one  of  the 
four  possible  minor  premises  will  yield  a definite  conclusion. 
Thus  we  have  the  proposition,  If  any  substance  turns  blue 
litmus  paper  red,  it  is  an  acid.  Here  antecedent  and  conse- 
quent are  reciprocally  related,  so  that  we  can  also  state  the 
proposition  conversely,  If  the  substance  is  an  acid,  it  will 
turn  blue  litmus  paper  red. 


144 


DEDUCTIVE  LOGIC 


With  such  a major  premise,  any  one  of  four  conclusions 
may  be  possible  according  as  the  antecedent  is  affirmed  or 
denied,  or  as  the  consequent  is  affirmed  or  denied. 

It  is  possible,  moreover,  to  transform  any  hypothetical 
proposition  into  a categorical  form.  Let  us  take  the  hypo- 
thetical, If  the  patient  takes  this  medicine,  he  will  get  well. 
The  two  minor  premises  which  give  indeterminate  conclu- 
sions are  as  follows  : — 

(1)  He  does  not  take  the  medicine. 

.-.  Conclusion  is  left  in  doubt. 

(2)  He  gets  well. 

.-.  Conclusion  is  left  in  doubt. 

Forming  these  into  categorical  syllogisms,  we  have : — 

(1)  The  taking  of  this  medicine  will  restore  health. 

The  patient  does  not  take  the  medicine. 

.-.He  will  not  be  restored. 

(2)  The  taking  of  this  medicine  will  restore  health. 

The  patient’s  health  is  restored. 

.-.  He  has  taken  the  medicine. 

By  examining  these  two  conclusions,  obviously  invalid,  it 
will  be  seen  that  the  denial  of  the  antecedent  in  a hypotheti- 
cal syllogism  is  equivalent  to  the  illicit  process  of  the  major 
term  in  the  categorical  syllogism,  and  the  affirmation  of  the 
consequent  is  equivalent  to  the  undistributed  middle  in  the 
same.  The  inferences  which  are  always  possible  in  the  hypo- 
thetical syllogism,  the  affirmation  of  the  antecedent,  or  the 
denial  of  the  consequent, are  designated  by  the  Latin  phrases, 
modus  ponens  and  modus  tollens  respectively. 

The  Disjunctive  Syllogism.  — In  this  syllogism  we  have  as 
major  premise  a disjunctive  proposition  of  the  form,  A is 
either  B or  C.  There  are  four  possible  minor  premises,  — 
being  the  affirmation  or  the  denial  of  either  one  of  the  alter- 
natives. The  conclusions  which  are  possible  depend  upon 


THE  DISJUNCTIVE  SYLLOGISM 


145 


the  nature  of  the  disjunctive  major  premise.  There  are 
the  following  cases : — 

(1)  If  the  disjunction  is  a strictly  logical  one, — that  is, 
the  terms  mutually  exclusive  and  the  disjunction  complete,1 
— then  the  affirmation  of  either  alternative  necessitates  as  a 
conclusion  the  denial  of  the  other,  while  the  denial  of  either 
one  necessitates  the  affirmation  of  the  other.  The  former  is 
called  the  modus  ponendo  tollens,  i.e.  the  mood  which  denies 
by  affirming ; the  latter  is  called  modus  tollendo  ponens,  i.e. 
the  mood  which  affirms  by  denying. 

(2)  If  the  disjunctive  members  are  not  mutually  exclu- 
sive, the  affirmation  of  the  one  does  not  necessarily  deny  the 
other.  Thus  we  might  have  the  disjunctive  proposition, 
The  disease  is  either  pneumonia  or  typhoid  fever.  The 
assertion  that  it  is  pneumonia  does  not  necessarily  render 
the  typhoid  fever  an  impossibility ; for  a patient  may  have 
both  diseases  at  the  same  time. 

(3)  If  the  disjunction  is  not  complete,  then  the  denial  of 
one  member  of  the  disjunction  does  not  necessitate  the 
affirmation  of  the  other,  for  one  or  more  possibilities  not 
expressed  in  the  original  disjunctive  statement  must  be 
reckoned  with.  For  instance,  let  us  take  the  disjunctive 
syllogism,  The  prices  of  commodities  will  be  either  in- 
creased or  lowered  by  this  law. 

They  cannot  be  increased. 

They  must  be  lowered. 

It  may  be  shown  that  there  is  a third  possibility,  namely,  the 
law  does  not  affect  the  prices  one  way  or  the  other. 

The  Dilemma.  — This  is  a complex  syllogism  in  which 
both  hypothetical  and  disjunctive  propositions  are  combined. 
The  dilemma  in  its  most  complete  form  is  constructed  as 
follows : the  major  premise  consists  of  two  hypothetical 
propositions,  — the  minor  premise,  of  a disjunctive ; and  the 
conclusion,  of  a disjunctive. 

1 See  p.  51. 


146 


DEDUCTIVE  LOGIC 


The  minor  premise  may  take  either  one  of  two  forms.  It 
may  affirm  disjunctively  the  two  antecedents  contained  in 
the  double  hypothetical  of  the  major  premise;  or  it  may 
deny  disjunctively  the  two  consequents  contained  in  the 
same.  If  the  former,  the  dilemma  is  called  constructive; 
if  the  latter,  destructive.  The  symbolic  representation  of 
these  two  forms  may  be  expressed  as  follows : — 

(1)  The  constructive  dilemma. 

If  A is  B,  C is  D ; if  ^7  is  F,  G is  H. 

Either  A is  B,  or  E is  F. 

C is  D,  or  G is  H. 

(2)  The  destructive  dilemma. 

If  A is  B,  C is  D ; if  E is  F,  G is  H. 

Either  C is  not  D,  or  G is  not  H. 

•\  Either  A is  not  B,  or  E is  not  F. 

The  above  being  the  complete  form  of  the  dilemma,  there 
may  be  certain  variations  introduced,  as,  for  instance,  instead 
of  two  consequents  there  may  be  only  one,  or  instead  of  two 
antecedents  there  may  be  only  one.  The  principle  of  the 
dilemma  is,  however,  not  affected  by  these  changes.  This 
principle  is  essentially  that  of  presenting  two  possibilities 
with  definitely  determined  consequences,  so  that  a choice 
must  be  made  between  them  which  in  either  case  results  in 
embarrassment,  confusion,  or  contradiction.  The  following 
dilemma,  which  will  serve  as  a type  of  dilemmas  in  general, 
illustrates  these  various  features  : — 

If  the  charges  of  the  Senator  from  South  Carolina  are 
true,  I am  unfit  to  remain  a member  of  the  Senate ; and  if 
they  are  untrue,  the  man  who  made  them  is  unfit  to  remain 
a member  of  this  honorable  body. 

But  they  must  be  true  or  untrue. 

Either  the  Senator  from  South  Carolina  is  unfit  or  I 
am  unfit  to  remain  a member  of  this  body.1 

1 Extract  from  a speech  of  Senator  McLaurin  in  answer  to  Senator 
Tillman’s  charges. 


THE  DILEMMA 


147 


It  will  be  observed  that  the  minor  premise  of  a dilemma 
states  the  possibilities  to  which  a given  situation  gives  rise, 
and  the  major  premise  states  the  necessary  relations  which 
these  possibilities  respectively  sustain. 

There  are  two  parts  of  a dilemma  where  a structural 
weakness  is  apt  to  occur,  which  of  course  affects  seriously 
the  validity  of  the  conclusion.  The  one  weakness  is  an 
absence  of  necessary  sequence  between  antecedent  and 
consequent  in  either  one  or  both  of  the  hypothetical 
propositions  which  form  the  major  premise.  The  other 
is  the  incompleteness  of  the  disjunctive  proposition  which 
forms  the  minor  premise.  If  the  alternatives  are  not 
mutually  exclusive,  or  if  they  are  not  exhaustive,  error  of 
course  must  result.  Sometimes  a specious  argument  in 
the  form  of  a dilemma  may  be  suddenly  presented  by  an 
opponent  in  controversy  or  in  debate,  and  produce  a tempo- 
rary confusion  of  mind  because  it  is  not  known  just  where 
the  fallacy  of  the  dilemma  is  concealed.  It  is  well  to  know 
therefore  the  exact  sources  whence  errors  in  the  dilemma 
are  apt  to  proceed. 

When,  in  the  major  premise  of  a dilemma,  the  conse- 
quents do  not  invariably  follow  from  the  given  antecedents, 
or  when  other  consequents  also  may  follow  which  are  not 
mentioned  in  the  premise,  then  it  is  possible  to  form  a 
counter  dilemma  which,  starting  from  the  same  premises, 
reaches  an  opposite  conclusion.  Both  the  original  dilemma 
and  the  counter  dilemma  in  such  cases  are  at  fault,  because 
they  both  start  from  an  inadequately  expressed  hypotheti- 
cal relation.  An  illustration  of  this  is  found  in  the  classi- 
cal incident  of  the  Athenian  mother  who  advised  her  son 
not  to  enter  public  life ; “ for,”  said  she,  “ if  you  act  justly, 
men  will  hate  you,  and  if  you  act  unjustly,  the  gods  will 
hate  you  ; but  you  must  act  either  justly  or  unjustly  ; there- 
fore public  life  will  result  in  your  being  hated.”  The  son, 
however,  brought  in  rebuttal  an  equally  plausible  state- 
ment; “ If  I act  justly,  the  gods  will  love  me;  and  if  I 


148 


DEDUCTIVE  LOGIC 


act  unjustly,  men  will  love  me ; therefore,  entering  public 
life  will  make  me  beloved.” 

Trilemma.  — There  is  a still  more  complex  form  of  the 
combined  hypothetical  and  disjunctive  propositions  which 
is  known  as  the  trilemma.  As  the  name  indicates,  the  dis- 
junction in  the  minor  premise  consists  of  three  members. 
This  is  illustrated  in  the  following  statement  regarding  the 
Louisiana  Purchase.  It  is  averred  that  the  sale  of  Louisiana 
to  the  United  States  was  invalid ; because,  if  it  were  French 
property,  Buonaparte  could  not  constitutionally  alienate  it 
without  the  consent  of  the  Chambers ; if  it  were  Spanish 
property,  he  could  not  alienate  it  at  all ; if  Spain  had  the 
right  of  reclamation,  the  sale  was  worthless. 


CHAPTER  XVIII 


EXTRA-SYLLOGISTIC  REASONING 

The  syllogism,  as  we  have  seen,  is  a form  of  inference 
which  is  essentially  the  interpretation  of  a special  case  in 
the  light  of  a universal  concept  to  which  it  can  be  referred. 
The  function  of  the  major  premise  is  the  statement  of  the 
universal  principle  or  relation  which  forms  the  basis  of  the 
inference;  that  of  the  minor,  the  statement  of  the  connec- 
tion of  the  special  case  under  consideration  to  this  universal ; 
that  of  the  conclusion  the  investiture  of  the  special  case 
with  the  essential  properties  which  belong  to  the  universal. 
Now  there  are  certain  forms  of  reasoning  which  do  not  ex- 
plicitly at  least  conform  to  this  programme  of  the  syllogism, 
and  which  judged  by  the  formal  rules  of  the  syllogism  must 
be  regarded  as  invalid,  but  which  nevertheless  are  commonly 
employed  in  our  everyday  inferences  and  whose  validity  is 
indisputable. 

There  is  in  the  first  place  the  so-called  reasoning  from 
“particulars  to  particulars.”  John  Stuart  Mill,  as  is  well 
known,  attacks  the  accepted  view  of  the  syllogism  insisting 
that  the  reasoning  process  is  never  based  upon  a complete 
universal,  but  always  starts  with  particulars  and  concludes 
with  particulars.1 

In  this  connection,  he  gives  the  following  illustrations : — 

“ It  is  not  only  the  village  matron  who,  when  called  to  a 
consultation  upon  the  case  of  a neighbour’s  child,  pronounces 
on  the  evil  and  its  remedy,  simply  on  the  recollection  and 
authority  of  what  she  accounts  the  similar  case  of  her  Lucy. 

1 Mill’s  Logic,  Book  II,  Chap.  Ill,  § 3. 

149 


150 


DEDUCTIVE  LOGIC 


We  all,  when  we  have  no  definite  maxims  to  steer  by,  guide 
ourselves  in  the  same  way;  and  if  we  have  an  extensive 
experience  and  retain  its  impressions  strongly,  we  may 
acquire  in  this  manner  a very  considerable  power  of  accu- 
rate judgment,  which  we  may  be  utterly  incapable  of  justify- 
ing or  of  communicating  to  others.  Among  the  higher 
order  of  practical  intellects,  there  have  been  many  of 
whom  it  was  remarked  how  admirably  they  suited  their 
means  to  their  ends  without  being  able  to  give  any  sufficient 
reasons  for  what  they  did ; and  applied,  or  seemed  to  apply, 
recondite  principles  which  they  were  wholly  unable  to  state. 
This  is  a natural  consequence  of  having  a mind  stored  with 
appropriate  particulars,  and  having  been  long  accustomed 
to  reason  at  once  from  these  to  fresh  particulars,  without 
practising  the  habit  of  stating  to  oneself  or  to  others  the 
corresponding  general  propositions.  An  old  warrior,  on  a 
rapid  glance  at  the  outlines  of  the  ground,  is  able  at  once 
to  give  the  necessary  orders  for  a skilful  arrangement  of 
his  troops ; though  if  he  has  received  little  theoretical  in- 
struction, and  has  seldom  been  called  upon  to  answer  to  other 
people  for  his  conduct,  he  may  never  have  had  in  his  mind 
a single  general  theorem  respecting  the  relation  between 
ground  and  array.  But  his  experience  of  encampments, 
under  circumstances  more  or  less  similar,  has  left  a number 
of  vivid,  unexpressed,  ungeneralized  analogies  in  his  mind, 
the  most  appropriate  of  which,  instantly  suggesting  itself, 
determines  him  to  a judicious  arrangement.” 

Mr.  Mill  is  no  doubt  quite  correct  in  this  outline  which 
he  sketches  of  common  procedure  in  inference.  However, 
it  cannot  be  claimed,  and  Mr.  Mill  is  the  last  one  to  claim 
it,  that  every  particular  instance  furnishes  sufficient  ground 
for  an  inference  concerning  a similar  particular  instance. 
On  the  contrary,  it  is  only  the  particular  instance  of  a cer- 
tain well-defined  kind  which  can  give  to  such  an  inference  the 
proper  logical  warrant  and  validity.  And  this  special  kind 
is  one  in  which  the  particular  instance  ranks  as  a typical 


EXTRA-SYLLOGISTIC  REASONING 


151 


case.  It  stands  in  one’s  thought  as  the  representative  of  the 
universal  of  which  it  is  a special  case.  In  our  reasoning  we 
speak  of  it  in  terms  of  its  particularity,  but  the  correspond- 
ing universal  is  always  in  the  background  of  thought,  and 
it  invests  the  particular  case  with  its  essential  significance. 
The  particular  is  merely  a disguised  universal.  The  partic- 
ular as  mere  particular  is  barren  of  any  inferential  result. 
When  however  it  stands  as  representative  of  the  universal 
of  which  it  is  a special  case,  then  it  serves  as  a valid  ground 
of  inference.  When  the  village  matron  argues  from  her 
own  child’s  case  to  that  of  some  other  child,  she  has  in  mind, 
dimly  it  may  be,  but  nevertheless  truly,  some  idea  which 
embraces  her  child’s  case  and  her  neighbor’s  in  one  and  the 
same  class.  She  knows,  although  it  may  not  be  explicit  in 
her  thought,  that  the  cure  of  the  child  did  not  depend  upon 
any  circumstance  peculiar  to  her  constitution  or  nature,  but 
that  the  treatment  employed  possessed  some  essentially 
efficacious  tendency  of  a universal  nature. 

When  the  argument  is,  however,  narrowed  down  to  a 
single  special  case,  and  this  is  made  the  basis  of  an  infer- 
ence to  another  case  which  closely  resembles  it,  then  we 
have  inference  by  analogy.1  There  is  a marked  difference 
between  the  special  case  which  furnishes  ground  for  infer- 
ence, because  it  stands  in  our  minds  as  a typical  case  repre- 
sentative of  its  appropriate  universal,  and  on  the  other  hand 
that  special  case  which  does  not  imply  a universal  at  all, 
but  immediately  suggests  some  resemblance  to  a similar 
case  and  thus  opens  the  way  for  reasoning  by  analogy. 
Analogy,  as  a form  of  inference,  has  attached  to  it  an  element 
of  uncertainty  so  long  as  its  basis  is  merely  a particular 
instance.  When  that  particular  instance  begins,  however, 
to  assume  the  characteristics  of  a typical  case,  and  to  direct 
the  thought  to  its  corresponding  universal,  then  inference 
by  analogy  passes  over  by  insensible  degrees  to  the  ordinary 
syllogistic  inference,  or  inference  by  subsumption. 

1 See  p.  186. 


152 


DEDUCTIVE  LOGIC 


There  is,  again,  another  form  of  inference,  which  departs 
from  the  syllogistic  type  but  which  nevertheless  possesses 
undoubted  logical  validity,  such  as  the  following : — 

A is  to  the  right  of  B. 

B is  to  the  right  of  C. 

A is  to  the  right  of  C. 

Judged  strictly  by  the  logical  rules  of  the  syllogism,  the 
above  conclusion  is  invalid,  because  the  given  syllogism  has 
four  terms,  A,  B,  the  right  of  B,  and  the  right  of  C.  There 
is,  therefore,  no  proper  middle  term  ; for  B and  to  the  right 
of  B are  different  and  can  give  no  identical  point  of  refer- 
ence for  the  two  premises.  Nevertheless  this  syllogism 
holds.  No  one  would  think  of  denying  its  validity.  How- 
ever, its  form  alone  does  not  warrant  the  conclusion ; for  we 
may  construct  a syllogism  of  the  same  form  whose  conclu- 
sion is  invalid.  For  example, in  the  following  syllogism:  — 

A is  a friend  of  B. 

B is  a friend  of  C. 

A is  a friend  of  C. 

it  is  obvious  that  the  conclusion  does  not  follow  necessarily 
from  the  premises.  Again,  let  us  take  a concrete  example 
of  a line  of  argument  which  appeals  to  many  as  quite  cogent, 
but  is  nevertheless  evidently  fallacious,  such  as  the  fol- 
lowing: — 

Princeton  has  defeated  Yale  in  base-ball. 

Yale  has  defeated  Harvard. 

.-.  Princeton  will  defeat  Harvard. 

We  are  confronted  therefore  by  this  problem : — 

Given  the  following  syllogism, 

A sustains  certain  relations  to  B. 

B sustains  similar  relations  to  C. 

A must  sustain  these  same  relations  to  C. 


EXTRA-SYLLOGISTIC  REASONING 


153 


What  kind  of  relations  are  they  which  necessitate  such  a 
conclusion,  and  what  kind  are  they  which  leave  the  conclu- 
sion indeterminate ; or,  in  other  words,  what  are  the  precise 
criteria  which  will  differentiate  the  truly  logical  ground 
from  the  illogical  as  regards  the  nature  of  the  relations  upon 
which  the  inference  is  based  ? The  answer  is  not  far  to 
seek.  It  lies  in  the  very  nature  of  the  syllogistic  inference 
itself.  We  have  seen  that  every  valid  inference  must  pro- 
ceed from  premises  which  have  as  common  ground  some 
identical  point  of  reference.1  If  the  premises  are  not  joined 
at  a common  point  of  articulation,  their  logical  force  can- 
not be  combined,  and  without  the  premises  in  combination, 
no  conclusion  follows. 

Now,  in  the  syllogism  expressing  relations  of  a perfectly 
general  character  as  given  above,  the  form  alone  does  not 
give  this  necessary  point  of  common  reference.  We  must 
look,  therefore,  for  some  direct  test  as  regards  the  nature 
of  the  relations  as  there  expressed.  If  the  relation  which 
obtains  in  the  major  premise  is  the  same  as  that  which 
obtains  in  the  minor  premise,  then  evidently  this  identity 
of  relation  secures  the  desired  identical  point  of  reference, 
and  therefore  furnishes  logical  warrant  for  the  derived  con- 
clusion. This  identity  of  the  relations  obtaining  in  the  major 
and  minor  premises  can  be  established  indisputably,  however, 
only  when  these  relations  appear  in  a system  of  coordinated 
parts,  wherein  there  is  such  simplicity  that  the  relations 
of  part  to  part,  throughout  the  whole  extent  of  the  system, 
can  be  definitely  and  exhaustively  comprehended.  It  is 
only  simplicity  of  system  that  gives  necessity  of  inference. 
Otherwise  in  relations  which  seem  to  be  identical,  there 
may  lurk  some  unknown  and  essential  differences.  From 
the  premises  that  A is  a friend  of  B,  and  that  B is  a friend 
of  C,  the  conclusion  that  A is  a friend  of  C does  not  fol- 
low because  the  system  in  which  these  relations  obtain 
is  so  exceedingly  complex  as  to  allow  the  possibility  of  a 
1 Bosanquet,  Essentials  of  Logic,  p.  74  f. 


154 


DEDUCTIVE  LOGIC 


very  wide  divergence  between  phenomena,  which  upon  the 
surface  seem  quite  similar.  Not  so,  however,  with  the 
premises,  A is  to  the  right  of  B and  B to  the  right  of  C. 
The  conclusion  is  left  in  no  doubt,  for  the  very  reason  that 
the  given  relations  emerge  in  a system  so  simple  that  no 
new  or  unknown  elements  can  be  conceived  as  disturbing 
factors.  Think  however  of  introducing  a change  into  this 
simple  system.  Regard  it  no  longer  as  a plane  surface,  but 
as  the  surface  of  a sphere.  The  conclusion  from  the  given 
premises  does  not  follow  necessarily. 

Any  system,  therefore,  which  is  of  such  simplicity  as  to 
assure  the  identity  of  given  relations,  will  always  furnish 
a logical  ground  for  inferences  of  the  kind  we  have  been 
discussing.  Such  inference  is  called  inference  by  construc- 
tion rather  than  inference  by  subsumption.  It  is  inference 
by  construction  because  the  mind  takes  the  material  fur- 
nished by  the  premises,  and  places  it  where  it  belongs  in 
an  underlying  system  which  is  explicitly  or  implicitly 
assumed.  The  conclusion  follows  because  the  construction 
has  been  made  within  that  system  and  according  to  the 
possibilities  which  the  nature  of  that  system  imposes. 
With  any  other  system  such  a construction  would  not 
have  necessitated  the  same  conclusion.  The  conclusion  that 
the  square  on  the  hypothenuse  is  equal  to  the  sum  of  the 
squares  on  the  other  two  sides  follows  only  when  we  con- 
ceive our  right-angled  triangle  as  constructed  upon  a plane 
surface  and  not  upon  a sphere.  If  you  say  to  me,  “ You 
must  be  a friend  to  my  friend  because  you  are  a friend  to 
me,”  my  reply  would  be:  “Not  necessarily;  for  in  the  vast 
system  of  social  relations  exposed  to  the  many  perturba- 
tions arising  from  the  qualities  and  the  frailties  of  human 
nature  alike,  the  relation  of  friend  to  friend  is  too  com- 
plex, too  subtle,  too  profound,  to  furnish  any  simple  and 
constant  basis  of  inference.  There  is  here  something  more 
than  a matter  of  mere  magnitude  and  position.” 

In  addition  to  the  examples  already  given  there  are  many 


EXTRA-SYLLOGISTIC  REASONING 


155 


other  simple  systems,  which  for  the  most  part  grow  out  of 
the  fundamental  categories  of  thought,  and  which  provide 
a logical  ground  upon  which  one  may  construct  these  in- 
ferences of  relation. 

There  is  the  system  which  expresses  solely  the  relations 
of  degree,  in  which  it  is  possible  to  construct  inferences 
such  as  the  following : — 

A is  taller  than  B. 

B is  taller  than  C. 

A is  taller  than  C. 

There  is  also  the  simple  time  system,  giving  the  infer- 
ence : — 

A is  older  than  B. 

B is  older  than  C. 

A is  older  than  C. 

We  may  have  also  somewhat  more  complicated  relations 
within,  however,  an  exceedingly  simple  system,  as  the  fol- 
lowing will  show : — 

A and  B,  two  angles  of  a plane  triangle,  equal  together  95°. 

C,  the  third  angle,  must  equal  85°. 

These  illustrations  might  be  multiplied.  They  are,  how- 
ever, sufficient  to  render  clear  the  criteria  regarding 
all  inference  concerning  related  elements  of  one  and  the 
same  system.  Whenever  identity  of  relationship  can  be 
established,  a valid  inference  is  possible;  and  identity  of 
relationship  can  be  established  only  in  systems  of  such 
simplicity  that  no  unknown  elements  which  might  dis- 
turb the  given  relations  can  be  conceived.  Our  thought 
must  command  the  system ; otherwise  we  are  never  justi- 
fied in  using  that  system  as  a basis  of  reasoning.  It  should 
be  added,  however,  that  the  relations  given  in  the  premises 
may  be  exceedingly  complex,  provided  only  the  system  in 
which  they  inhere  remains  so  simple  that  our  knowledge 
commands  it  fully.  Thus,  in  geometry,  there  is  the  possi- 


156 


DEDUCTIVE  LOGIC 


bility  of  indefinitely  complex  constructions ; there  are  many 
steps  in  the  reasoning  process  from  the  statement  of  the 
theorem  to  the  joyful  stage  of  the  Q.  E.  D. ; nevertheless, 
there  must  remain  the  constant  simple  system  of  space  and 
magnitude  relations  which  constitutes  the  ground  of  it  all. 

There  is  no  limit  to  the  length  of  a series  which  may 
express  continued  relations.  We  may  have  a related  to  b, 
b to  c,  c to  d,  d to  e,  and  so  on.  The  relations  between 
proximate  terms  will  not  insure  like  relations  between  more 
remote  terms  necessarily.  Here  again  our  test  comes  to  the 
fore.  If  in  such  a series  the  underlying  system  is  so 
simple  as  to  render  the  various  relations  identical  in  kind, 
then  all  terms  of  the  series  are  brought  within  a closed  cir- 
cuit, as  it  were,  and  we  can  then  pass  in  thought  from  the 
first  to  the  last  term  as  well  as  from  the  first  to  the  second. 

There  is  still  another  kind  of  inference  which  is  based 
upon  the  nature  of  certain  given  relations  and  partakes  of  the 
general  characteristics  of  immediate  inference.  It  is  this, 
that  whenever  we  have  given  a judgment  of  the  form,  a is 
related  to  b,  the  given  relation  necessitates  a converse  rela- 
tion, b is  related  to  a.  The  converse  relation  is  not  identical, 
however,  with  the  given  relation,  but  has  an  essentially 
distinct  significance,  usually  of  an  opposite  nature.  For 
example,  we  have  given  A is  the  father  of  B,  therefore  B 
is  the  son  of  A;  New  York  is  east  of  Chicago,  therefore 
Chicago  is  west  of  New  York.  The  following  may  be  urged 
as  an  exception  to  the  statement  that  the  converse  relation 
differs  essentially  from  the  given  one:  A is  a friend  of  B, 
therefore  B is  a friend  of  A.  However,  this  is  only  a seeming 
exception,  for  even  in  the  relation  of  the  most  intimate  friend- 
ship conceivable,  the  attitude,  feeling,  or  disposition  of  one 
party  in  the  friendship  is  never  the  same  as  that  of  the  other. 
The  precise  nature  of  the  converse  relation  will  always  de- 
pend upon  the  nature  of  the  system  in  which  the  given 
relation  obtains.1 

1 See  Russell,  The  Principles  of  Mathematics,  Chap.  IX,  on  “ Relations.” 


CHAPTER  XIX 


FALLACIES 

Fallacies  or  errors  in  reasoning  may  be  formal  or  mate- 
rial. The  formal  fallacy  is  one  which  is  due  to  the  struc- 
ture of  the  reasoning  process  itself ; the  material  fallacy  is 
due  to  the  thought  which  underlies  the  structure.  The 
formal  fallacies  have  been  treated  indirectly  at  least  in 
reference  to  the  various  rules  of  the  syllogism,  the  violation 
of  which  of  course  results  in  a fallacy  of  this  kind.  It  will 
be  sufficient  at  this  juncture  merely  to  summarize  these 
fallacies,  the  most  important  of  which  are  as  follows : — 

1.  Undistributed  middle. 

2.  Illicit  process  of  the  major  or  minor  term. 

3.  Denying  the  antecedent,  or  affirming  the  consequent 
of  the  hypothetical  syllogism. 

4.  Inadequate  disjunction  of  the  several  members  of  the 
major  premise  in  the  disjunctive  syllogism ; that  is,  when 
these  members  are  not  exclusive  and  therefore  overlap. 

5.  The  incomplete  enumeration  of  possibilities  in  the 
major  premise  of  the  disjunctive  syllogism. 

The  material  fallacies  may  be  divided,  as  did  Aristotle, 
into  two  classes,  — those  fallacies  which  are  due  to  language 
(napa  ttjv  Ae|iv,  or  in  dictione)  ; and  those  which  are  due"  to 
certain  errors  in  the  content  of  thought  itself  rijs  \e£ews, 
or  extra  dictionem). 

The  fallacies  which  are  due  to  language  arise  from  the 
fact  that  both  in  single  words  and  in  syntactical  forms  there 
may  lurk  ambiguities  of  meaning.  Any  ambiguity  of  mean- 
ing in  the  course  of  reasoning  violates  the  fundamental  law 

157 


158 


DEDUCTIVE  LOGIC 


of  identity,  which  demands  that  a single  and  constant  sig- 
nificance should  attach  to  all  the  thought  elements  which  go 
to  make  up  the  data  and  the  processes  of  our  reasoning. 

The  fallacies  due  to  language  are  often  referred  to  as  fal- 
lacies of  ambiguity.  Their  violation  of  the  law  of  identity 
will  be  seen  in  the  several  instances  which  will  be  given. 
These  fallacies  are  as  follows : — 

1.  Equivocation.  4.  Division. 

2.  Amphiboly.  5.  Accent. 

3.  Composition.  6.  Figure  of  Speech. 

1.  Equivocation.  — This  fallacy  consists  in  using  a word 
or  a phrase  which  is  capable  of  a double  meaning,  as,  for 
example : — 

I have  the  right  to  publish  my  opinions  concerning  the 
present  administration. 

What  is  right  for  me  to  do,  I ought  to  do. 

.-.  I ought  to  publish  my  opinions  concerning  the  present 
administration. 

The  ambiguity  here,  of  course,  lies  in  the  meaning  of  the 
word  right,  which  in  the  one  premise  is  to  be  taken  in  a 
legal  sense,  and  in  the  other  in  a moral  sense. 

This  fallacy  is  in  reality  a fallacy  of  four  terms  ; that  is, 
in  every  syllogism  there  should  be  only  three  terms,  each 
term  however  being  repeated.  The  law  of  identity  de- 
mands that  in  this  repetition  the  integrity  of  significance, 
as  regards  the  repeated  term,  must  be  preserved.  To  intro- 
duce a term,  therefore,  which  is  ambiguous  violates  this 
fundamental  principle  of  thought.  The  law  of  identity, 
however,  it  must  be  remembered,  allows  a certain  margin  of 
variation  in  meaning,  provided  only  that  the  essential  sig- 
nificance of  the  thought  is  not  impaired.  There  is  often  a 
difference  of  opinion  as  to  whether  a change  in  meaning 
affects  the  essential  significance  of  a concept  or  not.  For 
instance,  let  us  consider  the  following  syllogism  : — 

Whatever  menaces  the  public  interests  should  be  pre- 
vented by  law. 


FALLACIES 


159 


The  Great  Northern  Securities  Merger  menaces  the  public 
interests. 

It  should  be  prevented  by  law. 

Here  the  question  is  raised,  Does  this  merger  menace  the 
public  interests  in  the  sense  that  it  should  be  punished  by 
law  ? And  that,  of  course,  is  the  point  upon  which  the 
argument  turns. 

2.  Amphiboly.  — This  is  a fallacy  in  which  the  ambiguity 
lies  in  the  syntax  of  the  proposition  rather  than  in  the  terms 
of  which  it  is  composed.  The  following,  taken  from  a notice 
in  the  New  York  Tribune,  will  illustrate  this  : — 

“ To-morrow  afternoon,  at  four  o’clock,  the  Kev.  J.  A. 
Francis  will  deliver  the  third  and  last  address  of  a series  of 
plain  talks  to  young  men  about  their  perils  at  the  East  86th 
St.  branch  of  the  Y.  M.  C.  A.”  The  conclusion  is  obvious. 

The  following  epitaph,  also  illustrating  this  same  fallacy, 
I discovered  several  years  ago  on  a tombstone  in  the  old 
burying-ground  at  Concord,  Massachusetts  : — 

“ Sacred  to  the  memory 
of 


After  living  with  her  husband  for  fifty-five 
years,  she  departed  in  the  hope  of  a better  life.” 

3.  Composition.  — This  is  the  fallacy  due  to  the  supposi- 
tion that  what  may  be  affirmed  of  individuals  separately 
may  also  be  affirmed  of  them  when  taken  together.  It  does 
not  follow,  for  instance,  that  because  the  members  of  a foot- 
ball team  are  all  individually  excellent  players,  therefore 
the  team  play  will  show  a similar  order  of  excellence.  This 
fallacy  is  also  illustrated  in  the  following  quotation  from 
John  Stuart  Mill:  — 

“No  reason  can  be  given  why  the  general  happiness  is 
desirable  except  that  each  person,  as  far  as  he  believes  it 
to  be  attainable,  desires  his  own  happiness.  . . . Each  per- 
son’s happiness  is  a good  to  that  person,  and  the  general 


100 


DEDUCTIVE  LOGIC 


happiness  therefore  a good  to  the  aggregate  of  persons.” 
It  does  not  follow,  however,  that  because  each  desires  his 
own  happiness,  therefore  all  desire  the  happiness  of  the 
whole.  The  root  of  this  fallacy  is  to  be  found  in  the  neglect 
of  the  distinction  between  the  distributive  and  the  collective 
use  of  a term.  A term  is  used  distributively  when  it  is  ap- 
plicable to  each  individual  of  the  class  separately;  but 
collectively  when  it  is  applicable  only  to  all  the  individuals 
which  compose  the  class  when  taken  together.  It  is  the  dif- 
ference between  “ all  ” meaning  each  one,  and  “ all  ” meaning 
all  together. 

4.  Division.  — This  is  the  converse  of  composition,  and 
consists  in  affirming  of  individuals  separately  what  is  true 
only  when  they  are  taken  together.  It  does  not  follow,  for 
instance,  that  because  a certain  board  of  directors  has  the 
reputation  of  being  exceedingly  conservative,  therefore  any 
individual  member  of  that  board  is  necessarily  conservative 
also. 

5.  Accent.  — This  is  a fallacy  due  to  the  undue  accentua- 
tion of  a word  or  clause  in  any  statement  so  as  to  create  an 
implication  which  the  bare  words  themselves  do  not  indi- 
cate, and  which,  moreover,  was  not  intended  by  the  author 
of  the  words.  To  quote  from  the  text  of  an  author  and  to 
italicize  certain  words  will  often  necessitate  an  interpreta- 
tion quite  foreign  to  the  author’s  mind.  This  is  often  done 
with  malice  aforethought,  and  is  an  eminently  unfair  and 
indefensible  liberty  to  take  with  the  thought  of  others. 

6.  Figure  of  Speech.  — This  is  a fallacy  of  using  different 
parts  of  speech  having  a common  root  as  though  they  had 
precisely  the  same  meaning.  The  fact  is,  however,  that  a 
noun  may  have  a certain  meaning,  while  an  adjective  derived 
from  the  same  root  will  have  acquired  a twist  of  meaning  or 
a subsidiary  significance  which  will  prevent  their  being  re- 
garded in  the  light  of  interchangeable  terms.  The  following, 
also  from  John  Stuart  Mill,  will  illustrate  this:  — 

“ The  only  proof  capable  of  being  given  that  an  object  is 


FALLACIES 


161 


visible  is  that  people  actually  see  it.  The  only  proof  that 
a sound  is  audible  is  that  people  hear  it.  . . . In  like  man- 
ner, I apprehend,  the  sole  evidence  it  is  possible  to  produce 
that  anything  is  desirable  is  that  people  do  actually  desire 
it.”  In  this  quotation,  the  relation  of  the  word  desirable 
to  desire  is  not  the  same  as  the  other  two  cited,  namely, 
the  relation  of  the  word  visible  to  the  word  see,  and  of 
audible  to  the  word  hear.  Visible  means  that  which  can  be 
seen ; audible  means  that  which  can  be  heard  ; but  desirable 
does  not  mean  that  which  can  be  desired,  — rather,  that 
which  ought  to  be  desired. 

We  come  now  to  the  second  division  of  the  material 
fallacies,  those  which  are  due  to  inconsistencies  of  thought 
rather  than  to  ambiguities  in  the  expression  of  the  thought. 
These  fallacies  are  as  follows  : — 

1.  Accident.  5.  Petitio  Principii. 

2.  Converse  Accident.  6.  Non  Causa  pro  Causa. 

3.  Ignoratio  Elenchi.  7.  Many  questions. 

4.  Non  Sequitur. 

1.  Accident.  — This  is  expressed  in  the  Latin  phrase,  a 
dicto  simpliciter  ad  dictum  secundum  quid. 

This  is  the  fallacy  of  reasoning  from  what  is  true  as  a 
general  statement  ( simpliciter ) to  the  same  statement  which 
is  restricted  or  conditioned  in  some  manner  ( secundum  quid). 

The  following  is  this  fallacy  of  accident : — 

Strychnine  is  a deadly  poison,  and  therefore  it  can  never 
be  used  as  a medicine. 

2.  Converse  Accident.  — This  is  expressed  in  the  Latin 
phrase,  a dicto  secundum  quid,  ad  dictum  simpliciter.  This 
is  the  fallacy  of  reasoning  from  that  which  may  be  true 
under  certain  conditions  or  limitations,  to  that  which  how- 
ever is  not  true  when  these  conditions  or  limitations  are 
removed.  This  is  illustrated  in  the  following  argument 
which  is  very  often  heard : — 

Certain  men  have  risen  to  prominent  positions  who  never 


162 


DEDUCTIVE  LOGIC 


had  a college  education  ; therefore  a college  education  is  un- 
necessary to  equip  a man  for  his  life’s  work. 

In  reference  to  these  two  fallacies,  there  is  a passage  in 
Lotze  which  is  of  interest,  and  which  is  well  worth  quoting 
here. 

“ Two  general  modes  of  fallacious  thought  are  developed 
by  the  habitual  commission  of  these  fallacies,  and  illustrate 
them  on  a grand  scale.  The  first  is  doctrinairism,  the  second 
narrow-mindedness.  The  doctrinaire  is  an  idealist  who  refuses 
to  see  that  though  ideas  may  be  right  in  the  abstract,  yet  the 
nature  of  the  circumstances  under  which  and  of  the  objects 
to  which  they  are  to  be  applied  must  limit  not  only  their 
practicability  but  even  their  binding  force.  The  narrow- 
minded, on  the  other  hand,  can  recognize  and  esteem  no 
truth  and  no  ideal,  even  the  most  universal^  valid,  except 
in  that  special  form  to  which  they  have  become  accustomed 
within  a limited  circle  of  thought  and  personal  observation. 
Life  is  a school  which  corrects  these  habits  of  mind.  The 
parochially  minded  man  sees  things  persist  in  spite  of  him- 
self in  taking  shapes  which  he  considers  unprecedented,  but 
he  finds  the  world  somehow  survives  it,  and  learns  at  last 
that  a system  of  life  may  be  excellent  and  precious,  but  that 
it  is  rash  from  that  to  argue  that  it  is  the  only  proper  mode 
of  orderly  existence.  And  the  enthusiast  for  ideals,  when 
he  sees  the  curtailment  which  every  attempt  at  realization 
inflicts  on  them,  learns  the  lesson  which  the  disjunctive 
theorem  might  have  taught  him.  Every  universal  P changes 
in  the  act  of  being  applied  from  something  that  held  sim- 
pliciter  into  something  that  holds  secundum  quid,  — changes 
from  P to  p,1  p, 2 or  p3;  to  refuse  to  accept  it  in  any  one  of 
these,  which  are  its  only  possible  shapes,  is  to  ask  that  it 
be  realized  under  a condition  which  even  logic  pronounces 
impossible.” 1 

3.  Ignoratio  Elenchi.  — This  is  a fallacy  which  consists 
primarily  in  an  ignorance  of  the  nature  of  refutation.  To 
1 Lotze’s  Logic,  Vol.  II,  p.  5,  Eng.  trans. 


FALLACIES 


163 


refute  an  argument,  its  logical  contradiction  must  be  es- 
tablished. Any  proof  which  falls  short  of  this  fails  in  its 
end.  The  nature  of  this  fallacy  has  been  enlarged  in  scope, 
so  as  to  comprise  any  argument  whatever  which  does  not 
squarely  meet  the  point  at  issue.  It  is,  in  many  cases,  not 
so  much  the  ignorance  of  the  point  at  issue,  as  purposely 
ignoring  the  point  at  issue.  It  is  a natural  method  of  argu- 
ment when  one  has  a weak  case.  Any  subterfuge  which 
withdraws  attention  from  the  point  at  issue  tends,  of  course, 
to  strengthen  the  weaker  side,  at  least  as  regards  the  plausi- 
bility of  its  position.  Suppose  a student  should  be  urged 
to  spend  more  time  upon  his  Latin  or  Greek,  and  he  should 
excuse  his  negligence  by  insisting  that  in  after  life  he  would 
never  find  any  practical  use  for  his  classics,  — this  would  be 
the  fallacy  of  ignoratio  elenchi. 

There  are  various  ways  in  which  this  fallacy  may  be 
illustrated,  as  follows : — 

(a)  Argumentum  ad  hominem.  — This  is  the  fallacy  wherein 
the  argument  is  diverted  from  the  merits  of  the  case  to  the 
character  or  the  position  of  one’s  opponent. 

( b ) Argumentum  ad  populum. — This  is  the  fallacy  of  ap- 
pealing to  the  passion  or  prejudice  of  an  audience,  rather 
than  to  their  reason.  It  is  essentially  the  argument  of  the 
demagogue. 

(c)  Argumentum  ad  ignorantiam.  — This  fallacy  consists  in 
taking  advantage  of  the  ignorance  of  the  person  or  persons 
addressed  who,  consequently,  lack  the  power  of  discrimina- 
tion between  the  true  and  the  false,  the  relevant  and  the 
irrelevant. 

(i d ) Argumentum  ad  verecundiam.  — This  is  an  appeal  to 
the  sentiment  of  veneration  for  authority,  instead  of  an  appeal 
directly  to  the  reason.  The  weight  of  great  names  is  with 
some  persons  the  most  convincing  of  all  arguments.  Logi- 
cally it  is  not  an  argument  at  all.  It  may  serve  to  confirm 
truth,  but  it  does  not  establish  it. 

(e)  Argumentum  ad  baculum.  — This  repudiates  all  argu- 


164 


DEDUCTIVE  LOGIC 


merit  and  resorts  to  force  in  order  to  establish,  one’s 
point. 

In  distinction  from  these  various  kinds  of  subterfuges  to 
avoid  a direct  facing  of  the  question,  there  is  the  argumen- 
tum  ad  rem,  or  the  argumentum  ad  judicum,  i.e.  arguing 
directly  to  the  point  at  issue.  All  lines  of  argument  should 
converge  to  this  central  point. 

4.  The  Fallacy  of  the  Consequent,  or  Non  Sequitur.  — This 
fallacy  was  defined  primarily  by  Aristotle  as  the  formal  error 
of  affirming  the  consequent.  It  has  received,  however,  in 
the  course  of  time,  a far  wider  application,  and  has  come  to 
be  applied  to  any  loose  argument  whatever,  in  which  the 
conclusion  does  not  seem  to  follow  from  the  premises.  It 
is  very  convenient  to  have  the  phrase  non  sequitur  where- 
with to  characterize  such  arguments. 

5.  Petitio  Principii.  — This  is  the  fallacy  of  begging  the 
question.  This  is  an  attempt  to  assume  the  conclusion 
without  any  attempt  whatever  to  prove  it.  According  to 
Aristotle  this  may  take  place  in  five  ways : — 

(1)  To  assume  the  point  at  issue  directly.  This,  however, 
cannot  be  done  without  resort  to  some  rhetorical  device  to 
conceal  the  absence  of  any  real  proof. 

(2)  To  assume  some  more  general  truth  which  involves 
the  point  at  issue. 

(3)  To  assume  particular  truths  which  it  involves. 

(4)  To  assume  the  component  parts  in  detail. 

(5)  To  assume  some  necessary  consequence  of  the  point  in 
question. 

As  an  illustration  of  begging  the  question,  take  the  fol- 
lowing extract  from  a speech  of  a member  of  the  House  of 
Commons : “ The  bill  before  the  House  is  well  calculated 
to  elevate  the  character  of  education  in  this  country,  for  the 
general  standard  of  instruction  in  all  our  schools  will  be 
raised  by  it.” 

Galileo  accuses  Aristotle  of  having  committed  this  fallacy 
in  his  argument  that  “ the  nature  of  heavy  things  is  to  tend 


FALLACIES 


165 


toward  the  centre  of  the  universe,  and  of  light  things  to  fly 
from  it ; therefore,  the  centre  of  the  earth  is  the  centre  of 
the  universe.” 

There  is  a special  form  of  this  fallacy  known  as  arguing 
in  a circle,  circulus  in  probanda.  This  is  an  attempt  to 
prove  a conclusion  to  follow  from  a premise,  when  in  truth 
the  premise  itself  depends  upon  the  truth  of  the  conclusion 
as  its  ground.  This  is  illustrated  in  the  following  statement 
taken  from  a letter  written  to  one  of  our  daily  journals 
quite  recently : “ The  left-handed  man  lacks  will  power, 
for,  if  not,  he  wouldn’t  be  left  handed.” 

6.  Non  Causa  pro  Causa.  — This  is  the  fallacy  of  regarding 
as  a cause  that  which  is  not  a cause.  It  is  due  to  the  lack 
of  discrimination  between  a mere  coincidence  and  a verit- 
able cause.  There  is  no  fallacy,  perhaps,  which  is  so  subtle 
as  this  one,  and  none  which  is  more  common.  As  an  exam- 
ple of  this  fallacy,  we  may  cite  the  exploded  hypothesis 
of  a mesmeric  fluid  to  account  for  the  various  well-known 
phenomena  of  hypnotism ; also  the  statement  that  nature 
abhors  a vacuum  to  account  for  the  rise  of  water  in  a 
pump ; or  the  belief  that  any  unusual  appearance  among 
the  heavenly  bodies,  as  that  of  a comet,  is  to  be  interpreted 
as  a portent  of  disaster.  Many  of  our  common  superstitions 
may  be  traced  to  this  fallacy.  Moreover,  inasmuch  as  the 
causal  relation  naturally  manifests  itself  in  the  form  of  a 
sequence,  there  is  a special  case  of  this  fallacy  which  con- 
sists in  the  confusion  of  mere  sequence  with  a causal  con- 
nection ; this  is  called  the  fallacy  of  post  hoc  ergo  propter  hoc. 
This  is  illustrated  in  the  belief  which  many  entertain,  that 
when  thirteen  sit  down  together  at  a common  board,  one 
of  the  number  will  surely  die  within  the  year;  or  in  the 
tendency  so  often  observable  to  attribute  the  financial  pros- 
perity or  distress  of  the  country  to  some  legislative  measure 
recently  enacted. 

7.  The  Fallacy  of  Many  Questions.  — A better  name  for 
this  would  be  the  Fallacy  of  a Double  Question,  for  it  con- 


166 


DEDUCTIVE  LOGIC 


sists  in  asking  a question  which  is  in  the  form  of  a single 
question,  but  which  should  have  been  put  in  the  form  of  two 
separate  questions.  The  question  which  is  asked  assumes 
that  another  question  has  been  already  asked  and  answered. 
This  fallacy  usually  takes  the  form  of  asking  a question 
about  an  assumed  fact  whereas  the  fact  is  itself  in  dispute. 
Thus  the  question,  How  much  do  you  pay  a certain  member 
of  your  athletic  team  for  his  services,  presupposes  of  course 
that  some  amount  is  certainly  paid. 

The  following  anecdote  which  appeared  recently  in  one  of 
our  daily  papers  also  illustrates  this  fallacy  : — 

“ Charles  Bradlaugh,  the  English  free-thinker,  once  en- 
gaged in  a discussion  with  a dissenting  minister.  He 
insisted  that  the  minister  should  answer  a question  by  a 
simple  ‘Yes’  or  ‘No,’  without  any  circumlocution,  assert- 
ing that  every  question  could  be  replied  to  in  that  manner. 

“The  reverend  gentleman  rose,  and- said,  ‘Mr.  Bradlaugh, 
will  you  allow  me  to  ask  you  a question  on  those  terms  ? ’ 

“ ‘ Certainly/  said  Bradlaugh. 

“‘Then,  may  I ask,  have  you  given  up  beating  your 
wife  ? ’ ” 

This  completes  the  table  of  fallacies  usually  given  in 
treatises  on  logic.  All  the  general  types  of  fallacies  are 
comprehended  in  it.  There  are  fallacies,  however,  which  do 
not  distinctively  fall  under  any  one  type,  but  are  so  subtly 
complex  as  to  involve  the  errors  of  many.  There  are,  again, 
others  which  arise  out  of  special  circumstances,  and  cannot 
be  classified  under  any  of  the  types  mentioned.  They,  how- 
ever, readily  disclose  themselves  to  the  open  mind  which  is 
freed  from  sophistry  and  prejudice. 


PART  II 


INDUCTIVE  LOGIC 


CHAPTER  I 


INDUCTION  AND  DEDUCTION 

There  have  been  divergent  tendencies  in  the  history  of 
logic,  to  make  either  deduction  or  induction  alone  the  whole 
of  logical  procedure  in  the  process  of  inference.  The  fact 
that  the  Aristotelian  logic,  which  is  essentially  deductive, 
has  been  for  centuries  exclusively  associated  with  logic  as 
a whole,  has  left  the  impression  upon  many  minds  that  it 
is  the  beginning  and  end  of  the  logical  encyclopsedia.  On 
the  other  hand,  John  Stuart  Mill  and  his  followers  have 
attempted  to  analyze  the  syllogism  so  as  to  prove  its  es- 
sentially inductive  character;  and  they  maintain  that  all 
reasoning  is  inductive.  This  is  the  position  in  the  main  of 
Bacon,  Locke,  and  Bain.  Locke,  for  instance,  insists  that 
the  syllogism  is  of  less  value  than  external  and  internal 
experience,  induction,  and  common  sense.1 

So  also,  in  a similar  vein,  Schleiermacher  says : “ The 
syllogistic  procedure  is  of  no  value  for  the  real  construc- 
tion of  judgments,  for  the  substituted  judgments  can  only 
be  higher  and  lower;  nothing  is  expressed  in  the  conclu- 
sion but  the  relation  of  two  terms  to  each  other,  which 
have  a common  member,  and  are  not  without,  but  within, 
each  other.  Advance  in  thinking,  a new  cognition,  cannot 
originate  by  the  syllogism ; it  is  merely  the  reflection  upon 
the  way  in  which  we  have  attained,  or  could  attain,  to  a 
judgment,  the  conclusion ; no  new  insight  is  ever  reached.” 2 
The  two  opposed  views  thus  indicated  do  not  necessitate 
conflicting  or  mutually  exclusive  processes.  It  is  better  to 

1 Essay  on  Human  Understanding,  Book  IV,  p.  7. 

2 See  Ueberweg,  System  of  Logic,  etc.,  p.  345. 

169 


170 


INDUCTIVE  LOGIC 


regard  them,  not  as  radically  different  types  of  inference, 
but  rather  as  different  phases  of  one  and  the  same  inferential 
process.  We  have  seen  that  inference  consists  in  interpreting 
the  implications  of  the  system  to  which  the  given  in  con- 
sciousness belongs.  In  the  light  of  this  definition  we  can 
best  indicate  the  relative  functions  of  induction  and  deduc- 
tion in  the  process  of  inference.  When  the  system  can  be 
considered  as  a whole,  and  is  apprehended  in  its  entirety, 
then  it  may  become  the  ground  upon  which  the  inference  is 
based,  resulting  in  unfolding  the  necessary  nature  or  relations 
of  any  of  the  parts  considered  in  themselves,  or  in  reference 
to  the  system  as  a whole.  The  procedure  in  such  a case 
is  from  the  nature  of  the  whole  system,  to  the  nature  of 
the  several  parts,  and  their  existent  relations,  and  this  is 
deductive  in  its  essential  features. 

On  the  other  hand,  when  we  know  the  various  parts,  and 
proceed  from  them  as  data  to  construct  the  system  which 
their  known  nature  and  relations  necessitate,  it  is  induction, 
or  procedure  from  elementary  parts  to  the  whole  thus  neces- 
sitated. From  a knowledge  of  the  planetary  system  we 
can  infer  the  necessary  positions  of  sun,  moon,  and  earth 
at  any  required  time,  as,  for  instance,  in  the  calculation  of 
an  eclipse.  This  is  deduction.  But  when  we  begin  with 
investigating  the  several  movements  of  the  different  planets, 
and  from  them  infer  the  necessary  nature  of  the  system  of 
which  they  are  parts,  we  have  the  process  of  induction. 
Such  processes  we  see  must  be  complementary,  and  mutu- 
ally dependent.  As  Lavater  says,  “ He  only  sees  well  who 
sees  the  whole  in  the  parts,  and  the  parts  in  the  whole.’’ 

Moreover,  the  distinction  between  deduction  and  induc- 
tion may  be  shown  through  their  respective  relations  to  the 
universal,  which  we  have  seen  is  the  ground  of  inference. 
The  question  whose  answer  leads  to  the  deductive  process 
in  reasoning,  is,  What  does  the  universal  necessitate  ? In 
induction,  the  question  which  starts  the  investigation  is, 
Into  what  system  may  the  given  material  properties  or 


INDUCTION  AND  DEDUCTION 


171 


relations  be  constructed  so  as  to  reach  a universal  concept 
that  will  be  consistent  with  itself  and  with  the  whole  of 
knowledge  which  forms  the  world  of  consciousness  ? In 
this  there  is  an  analytical  discrimination  of  the  essential 
from  the  accidental  elements,  and  the  gathering  together  of 
the  former  into  the  complex  whole  which  is  the  universal. 
Induction,  therefore,  is  inference  viewed  from  the  side  of 
the  differences ; deduction  is  inference  viewed  from  that 
of  the  universal.  For  instance,  we  may  investigate  the 
characteristic  features  of  a diamond,  and  find  that  a certain 
specific  gravity,  3.53  as  compared  with  water,  is  a con- 
stant and  determining  attribute,  and  as  such  must  be  in- 
corporated as  an  essential  element  of  the  general  concept 
diamond.  We  can  then  form  the  universal  judgment,  What- 
ever stones  possess  this  specific  gravity  are  diamonds.  Their 
differences,  regarding  size,  brilliancy,  etc.,  may  all  be  set 
aside  as  accidental,  but  the  one  constant  determining  fea- 
ture indicates  a oneness  in  which  they  all  agree. 

And  so  with  the  other  essential  attributes.  After  pos- 
sessing such  knowledge  gained  inductively,  we  may  use  it 
practically  in  a deductive  manner ; and  it  is  so  used  in 
discriminating  between  true  and  imitation  stones,  as  de- 
scribed in  the  following  process : “ Diamonds,  rubies,  and 

sapphires  are  now  tested  by  floating  to  prove  their  genuine- 
ness. The  liquid  used  has  five  times  the  density  of  water, 
and  is  composed  of  double  nitrate  of  silver  and  thallium. 
The  tests  are  rapidly  made,  as  all  stones  of  the  same  nature 
have  the  same  specific  gravity,  while  none  of  the  bogus  ones 
have  the  same  weight  as  those  they  are  made  to  imitate.” 

Another  view  of  the  relation  of  induction  to  deduction 
may  be  gained  by  calling  attention  to  the  difference  of  sig- 
nificance between  the  terms,  a “truth”  and  a “ fact.”  A fact 
carries  with  it  only  the  special  and  individual  character  of 
the  particular  occurrence  in  which  it  is  manifested.  A 
truth,  however,  is  always  universal  in  its  very  nature,  ad- 
mitting of  universal  application,  and  capable  of  illustration 


172 


INDUCTIVE  LOGIC 


in  an  indefinite  number  of  different  facts  which  embody  its 
essence.  In  deduction  we  have  given  some  truth  of  uni- 
versal nature  that  leads  to  individual  facts  that  may  be 
subsumed  under  it.  In  induction,  we  interpret  a fact  or  a 
number  of  facts  in  the  light  of  their  universal  implication, 
on  the  ground  that  there  can  be  no  such  thing  as  an  isolated 
fact,  but  every  fact  must  have  some  relation  to  a universal 
to  which  it  must  be  referred. 

While  considering  the  distinctions  between  induction  and 
deduction,  we  must  not  overlook  their  mutual  dependence. 
We  cannot  proceed  in  deduction  irrespective  of  induction, 
because  the  universal  upon  which  the  deductive  process  is 
based  arises  in  the  majority  of  cases  from  a previous  induc- 
tion. It  is  true  that  the  universal  term,  may  be  in  a propo- 
sition that  is  known  a priori,  as  the  axioms  of  geometry  and 
certain  space  and  time  postulates  ; but  a very  small  propor- 
tion of  major  premises  can  be  said  to  have  such  an  origin, 
and  their  resulting  conclusions  have  very  slight  material 
significance.  Deduction  that  reaches  other  than  purely  ab- 
stract and  formal  conclusions  must  rest  upon  induction  for 
the  material  to  form  its  premises.  We  find  this  even  in 
the  technical  construction  of  the  syllogism,  where,  for  in- 
stance, the  question  of  the  distribution  of  the  terms  is 
raised.  We  may  insist  that  a certain  middle  term  is  dis- 
tributed, as  it  is  the  subject  of  an  universal  affirmative 
proposition ; but  then  the  further  question  naturally  sug- 
gests itself,  How  do  we  know  that  the  proposition  in  ques- 
tion is  really  a universal  ? Its  material  significance  alone 
tells  us  that  we  may  write  it  as  an  A or  I proposition,  as 
the  case  may  be.  The  matter  is  a function  of  the  form, 
and  the  form  a function  of  the  matter.  They  cannot  be 
separated,  in  fact,  unless  we  conceive  reasoning  as  a purely 
formal  process  of  determining  a conclusion,  irrespective  of 
the  truth  or  falsity  of  the  premises.  If  we  regard  the 
premises  as  given,  and  we  accept  them  with  unquestioning 
credence,  the  deduction  is  purely  formal ; so,  also,  if  the 


INDUCTION  AND  DEDUCTION 


173 


various  terms  are  expressed  by  letters  A,  B,  C,  etc.,  and 
devoid  of  any  material  significance.  Any  process  of  rea- 
soning based  upon  a slavish  acceptance  of  premises  can  only 
reach  artificial  and  even  false  results.  In  the  actual  experi- 
ences of  life  our  premises  are  not  made  for  us.  They  must 
be  constructed  by  us  through  our  interpretation  of  reality. 
Disregard  of  this  has  brought  formal  logic  into  much  disre- 
pute, and  it  has  often  degenerated  into  the  barren  discussion 
of  logical  puzzles  and  quibbles.  Grant  a person  any  prem- 
ises he  may  choose  to  assume,  irrespective  of  an  inductive 
test  of  their  validity,  he  can  prove  black  white  and  white 
black. 

On  the  other  hand,  induction  is  dependent  upon  deduction  ; 
for  we  cannot  reason  from  particular  instances  to  a universal 
proposition,  unless  we  assume  as  basis  of  the  whole  induc- 
tive process  some  postulate  which  has  real  universal  signifi- 
cance. Otherwise,  we  reach  only  a high  degree  of  probability, 
but  not  necessity;  a rude  generalization,  but  not  univer- 
sality. When  we  assert  some  such  general  statement  as 
this,  that  arsenic  always  acts  as  a poison,  we  have  based 
the  universal  character  of  the  proposition  upon  an  under- 
lying postulate  that  is  understood  even  though  it  is  not 
expressed,  such  as  the  uniformity  of  nature,  that  under 
identical  conditions  we  always  look  for  identical  effects. 
This  will  be  discussed  later  more  in  detail ; it  is  referred  to 
at  this  point  merely  to  illustrate  the  deductive  basis  of 
induction.  Bradley  insists  that  there  can  be  no  such  thing 
as  induction,  because  it  always  rests  upon  an  implied  uni- 
versal which  gives  to  the  process  as  a whole  a deductive 
character.1  His  criticism  has  the  force  only  of  proving  that 
induction  cannot  be  independent  of  deduction.  This  depend- 
ence does  not,  however,  necessarily  vitiate  the  integrity  of 
induction  as  a mode  of  the  inferential  process.  Lotze  has 
placed  special  emphasis  upon  this  dependemce  of  induction 
upon  deduction.  He  says : “ It  is  the  custom  in  our  day  to 
1 Bradley,  Principles  of  Logic,  p.  342. 


174 


INDUCTIVE  LOGIC 


collect  into  one  body  the  numerous  operations  which  assist 
us  in  ascending  from  particulars  to  generals,  or  to  call  this 
inductive  logic,  and  to  set  it  against  the  deductive  or  demon- 
strative logic  along  with  much  disparagement  of  the  latter. 
Such  disparagement  rests  on  a mistake.  The  inductive 
methods,  it  is  certain,  are  the  most  effectual  helps  to  the 
attainment  of  new  truth,  but  it  is  no  less  certain  that  they 
rest  entirely  on  the  results  of  deductive  logic.”  1 

Moreover,  in  induction  the  results  obtained  and  formulated 
in  general  propositions  may  be  extended  and  often  modified 
by  a deduction  which  is  based  upon  them  as  major  premises ; 
for  the  deduction  thus  proceeding  from  them  reveals  new 
instances  which  conform  or  perhaps  modify  the  simple 
inductive  results  themselves.  What  is  popularly  called  a 
hasty  generalization,  if  made  a major  premise  of  a syllo- 
gism, will  often  lead  us  astray  through  the  deductions 
drawn  from  it.  As  soon  as  we  are  aware  of  this,  we  return 
to  question  the  validity  of  the  generalization,  whose  weak- 
ness is  not  appreciated  until  thus  tested  and  revealed.  Thus 
deduction  serves  to  extend  and  correct  the  results  of  induc- 
tion, and  at  the  same  time  it  itself  is  dependent  upon  the 
results  of  inductive  generalization  for  the  material  to  form 
its  premises.  We  come  to  see  therefore  how  intimately 
associated  these  two  processes  are  in  actual  reasoning.  For 
convenience  of  illustrating  their  individual  characteristics, 
they  may  be  considered  as  separate,  and  each  investigated 
as  an  independent  mode  of  inference.  But  they  are  in  reality 
mutually  related  and  dependent,  and  are  always  found  mani- 
festing their  functions  together.  In  any  course  of  reasoning 
concerning  the  conduct  of  our  everyday  affairs,  or  in  sci- 
entific investigation,  — anywhere,  indeed,  outside  of  the 
artificial  examples  of  logical  text-books,  — we  reason  both 
inductively  and  deductively  in  one  complex  process. 


1 Lotze,  Logic,  p.  288.  See  also  Bosanquet,  Logic,  Vol.  II,  p.  119. 


CHAPTER  II 


THE  ESSENTIALS  OF  INDUCTION 

We  now  proceed  to  a more  precise  determination  of  the 
nature  of  induction.  Its  point  of  view  in  all  reasoning  has 
reference  to  concrete  instances.  They  are  the  data,  and 
from  them  general  propositions  are  to  result.  The  pro- 
cedure is  from  given  facts  to  laws  which  are  the  ground  and 
explanation  of  these  facts.  We  are  here  however  at  once 
struck  with  the  evident  break  in  the  course  of  our  reasoning. 
Procedure  from  the  particular  to  the  universal  cannot  be  a 
continuous  process.  There  is  a gap  somewhere.  The  con- 
clusion contains  more  than  the  premises.  In  deduction,  we 
are  proceeding  from  the  greater  to  the  less,  and  we  experi- 
ence no  violation  of  our  logical  sense ; but  at  once  we 
appreciate  the  difficulty  which  attends  the  reverse  process 
from  the  less  to  the  greater.1  Here  we  soon  reach  a point 
where  we  pass  beyond  the  sphere  of  our  experience  to  the 
generalization  which  necessarily  embraces  far  more  than 
our  experience.  This  is  the  so-called  inductive  leap ; or  it 
is  sometimes  referred  to  as  the  inductive  hazard.  But  is  this 
a leap  in  the  dark  — a wild  guess  concerning  all  that  lies 
beyond  the  sensuous  sphere  of  our  immediate  experience  ? 
This  would  be  the  case,  were  we  compelled  to  use  the  mere 
data  of  experience  as  sole  ground  for  our  inferences.  John 
Stuart  Mill  insists  that  nothing  whatever  is  given  in  con- 
sciousness but  particular  sensations,  and  these  are  but  sub- 
jective states  of  feeling,  and  with  no  assurance  of  any 
definite  correspondence  with  the  external  world.  With  such 
purely  empirical  data  it  is  impossible  to  proceed  to  truths  of 

i See  p.  107. 

175 


176 


INDUCTIVE  LOGIC 


universal  validity.  It  is  necessary  to  postulate  some  uni- 
versal truth  which  the  mind  through  strictly  a priori  con- 
siderations is  constrained  to  formulate,  and  which  will  serve 
to  bridge  the  gulf  between  the  particular  and  the  universal. 

This  postulate  has  been  variously  expressed  by  different 
authors,  yet  with  substantially  the  same  significance  in  all. 
In  the  older  logic,  it  is  put  under  the  convenient  formula  of 
the  uniformity  of  nature  ; that  is,  that  beyond  the  sphere 
of  experience,  phenomena  will  behave  in  the  same  manner 
under  like  conditions,  as  in  the  sphere  of  immediate  obser- 
vation and  experiment.  In  the  modern  logic  this  is  some- 
what differently  expressed.  The  phrase  “uniformity  of 
nature,”  being  somewhat  indefinite  and  implying  a point 
of  view  purely  objective,  is  not  used.  Modern  writers  have 
omitted  it  largely  from  their  terminology.  Lotze  says: 
“The  logical  idea  upon  which  induction  rests  is  by  no 
means  merely  probable,  but  certain  and  irrefragable.  It 
consists  in  the  conviction  based  upon  the  principle  of 
identity,  that  every  determinate  phenomenon  M can  depend 
upon  only  one  determinate  condition,  and  accordingly  that, 
where  under  apparently  different  circumstances  or  in  differ- 
ent subjects  P,  S,  T,  U,  the  same  M occurs,  there  must 
inevitably  be  in  them  some  common  element  2 which  is  the 
true  identical  condition  of  M,  or  the  true  subject  of  M.” 1 
We  have  a somewhat  similar  description  of  the  basis  of  the 
inductive  process  given  by  Sigwart:  “The  logical  justification 
of  the  inductive  process  rests  upon  the  fact  that  it  is  an  inevi- 
table postulate  of  our  effort  after  knowledge  that  the  given  is 
necessary,  and  can  be  known  as  proceeding  from  its  grounds 
according  to  universal  laws.”  2 Bosanquet  considers  as  the 
basis  of  inductive  inference  that  which  he  calls  the  postu- 
late of  knowledge,  that  “ the  universe  is  a rational  system, 
taking  ‘ rational  ’ to  mean  not  only  of  such  a nature  that  it  can 
be  known  by  intelligence,  but  further  of  such  a nature  that 
it  can  be  known  and  handled  by  our  intelligence.” 3 

1 Lotze,  Logic , p.  102.  2 Sigwart,  Logic  (Eng.  trans.),  Vol.  II,  p.  289. 

8 Bosanquet,  The  Essentials  of  Logic,  p.  166. 


ESSENTIALS  OF  INDUCTION 


17T 


I have  quoted  these  passages  from  Lotze,  Bosanquet,  and 
Sigwart,  that  we  may  appreciate  the  modern  tendency  to 
derive  the  inductive  postulate  from  an  epistemological 
source;  namely,  that  our  knowledge  must  be  consistent 
throughout  with  itself,  part  to  part,  and  parts  to  whole,  and 
that  the  world  for  us  is  the  world  as  constructed  by  our 
knowledge.  Whatever  is  given  in  consciousness  must  be- 
long therefore  in  the  one  place  where  it  appropriately  and 
necessarily  belongs.  Here  also  there  must  be  a place  for 
everything,  and  everything  in  its  place.  There  must  be  a 
uniformity  of  consciousness ; that  is,  the  primary  postulate 
and  the  uniformity  of  nature  is  secondary  to  this,  and 
implied  in  it.  This  postulate  may  also  be  expressed  as 
follows:  What  is  once  true  is  always  true.  Here  “true”  is 
used  in  the  sense  of  the  universal  significance  of  a fact. 
Whenever  a concrete  instance  is  present  in  consciousness,  its 
existence  must  be  considered  as  necessitated  by  some  ante- 
cedent which  can  satisfactorily  account  for  it,  and  which 
can  at  the  same  time  be  appropriately  adjusted  to  the  whole 
of  our  knowledge  in  interpreting  it.  Bosanquet  says  that 
“ ideally  speaking,  every  concrete  real  totality  can  be 
analyzed  into  a complex  of  necessary  relations.”1  These 
necessary  relations  of  course  have  a universal  significance, 
and  therefore  in  every  concrete  instance,  if  we  can  rightly 
interpret  it,  we  may  discern  the  universal  element  which  is 
contained  in  it,  and  gives  it  a place  and  meaning  in  the 
world  as  cognized  by  us.  Nature,  after  all,  is  only  another 
word  for  the  world  as  we  know  it. 

There  is  a sense  in  which  induction  may  be  regarded  as 
the  inverse  process  of  deduction.  In  deduction  the  problem 
is  concerned  with  the  question,  What  does  the  universal 
necessitate?  In  induction,  the  instance  is  given,  and  the 
problem  is,  What  universal  can  be  discovered  which  could 
give  rise  to  the  instance  in  question  ? This  view  of  induc- 
tion is  especially  associated  with  the  name  of  Jevons,  whose 
1 Bosanquet,  Logic,  Vol.  II,  p.  82. 


178 


INDUCTIVE  LOGIC 


inductive  system  is  described  as  the  inverse  of  deduction. 
He  calls  it  the  deciphering  of  the  hidden  meaning  of  natural 
phenomena.1  The  name  commonly  used  to  designate  this 
view  of  induction  is  that  of  “reduction,”  originally  sug- 
gested by  Duhamel.2  This  process  was  known  to  the  old 
logicians,  who  called  it  “ Method,”  to  denote  the  process  of 
hunting  for  middle  terms  by  the  aid  of  which  a given  con- 
clusion could  be  proved.3  Like  all  inverse  processes,  it  is 
by  itself  an  indeterminate  one. 

Given,  All  A is  B,  and 
All  B is  C, 

we  infer  by  the  direct  process  of  deduction  that 
All  A is  C. 

But  in  the  indirect  or  inverse  process  we  have  given  A is 
C,  and  the  problem,  to  find  a middle  term  which  necessi- 
tates such  a conclusion,  is  an  indeterminate  one.  There 
may  be  a number  of  middle  terms.  This  is  analogous  in 
one  respect  to  the  method  of  integral  calculus ; while  dif- 
ferentiation leads  to  a definite  result,  the  inverse  process  of 
integration  leads  to  an  indeterminate  result.  So  also  we 
multiply  two  numbers,  producing  one  determinate  result; 
but  inversely,  when  we  have  given  a certain  number,  and 
ask  what  factors  multiplied  together  could  produce  this 
number,  we  may  reach  several  different  solutions.  The 
answer  is  indeterminate.  Professor  Jevons,  in  his  scheme 
of  inductive  inference,  falls  back  upon  probability  to  indi- 
cate which  of  several  possibilities  is  the  most  likely  one  in 
the  given  case.4  But  before  the  inverse  operation  can  result 
in  determinate  results,  the  given  terms  such  as  A and  C 
must  be  subjected  to  some  analysis  in  order  that  their 
material  signification  may  give  suggestion  as  to  the  nature 

1 Jevons,  Principles  of  Science,  p.  124. 

2 Duhamel,  Methodes,  Vol.  I,  p.  24. 

3 Venn,  Empirical  Logic,  p.  361. 

4 Jevons,  Principles  of  Science,  p.  219. 


ESSENTIALS  OF  INDUCTION 


179 


of  the  middle  term.  For  instance,  a man  is  found  dead, 
washed  ashore  by  the  tide ; the  natural  supposition  would 
be  that  he  met  his  death  by  drowning.  And  yet  it  might 
possibly  happen  that  the  man  died  through  injuries  inflicted 
by  blows,  or  by  poison,  or  heart  failure.  The  attendant  cir- 
cumstances and  bodily  indications  must  suggest  the  most 
probable  cause  to  account  for  the  given  effect.  Venn  criti- 
cises Jevons’  view  of  induction,  that  is,  making  it  the 
inverse  process  of  deduction,  on  the  ground  that  it  is  purely 
a formal  process,  and  therefore  can  lead  only  to  indetermi- 
nate results.1 

It  is  always  possible,  however,  to  make  some  analysis  of 
the  material  significance  of  the  data,  as  has  been  above  indi- 
cated, which  relieves  the  purely  formal  processes  from  the 
indefiniteness  of  the  results.  Bosanquet  criticises  Jevons’ 
theory  of  inductive  inference,  in  that  the  hypothesis  pro- 
posed to  account  for  the  given  in  reality  can  at  best  be 
only  highly  probable.2  However,  Venn,  Lotze,  Bosanquet, 
Sigwart,  all  allow  a place  to  the  inverse  function  of  all 
inductive  reasoning ; their  contention,  however,  is  this,  that 
it  does  not  funish  an  adequate  account  of  the  whole  matter.3 

It  is  interesting  to  note  that  Whewell’s  theory  of  induc- 
tion corresponds  in  the  main  to  this  idea  of  reduction,  or 
inverse  process.  He  finds  in  induction  a twofold  operation 
of  the  mind,  consisting  in  the  colligation  of  facts  and  the 
explication  of  conceptions.  By  the  colligation  of  facts  he 
refers  to  that  insight  which  is  able  to  see  the  connections 
and  relations  which  necessarily  exist  between  the  different 
phenomena  present  in  consciousness ; and  by  explication  of 
conceptions  he  refers  to  the  appropriate  fitting  in  of  these 
related  facts  to  some  conception  of  the  mind  which  most 
readily  accounts  for  them.4  Such  a process  is  merely  the 

1 Empirical  Logic,  p.  359.  2 Bosanquet,  Logic,  Vol.  II,  p.  175. 

8 Venn,  361 ; Bosanquet,  Vol.  II,  p.  175  ; Sigwart,  Vol.  II,  p.  203,  289. 

Lotze,  Outlines  of  Logic,  p.  93. 

4 Whewell,  Philosophy  of  the  Inductive  Sciences,  pp.  172,  202. 


180 


INDUCTIVE  LOGIC 


reading  of  given  facts  backward  to  their  origin,  or  substan- 
tially an  inverse  process,  where  the  procedure  is  from  the 
given  concrete  to  the  explanation  of  the  same  in  terms  of  the 
universal  to  which  it  can  be  most  appropriately  referred. 
So  also  Mill’s  account  of  procedure  by  hypothesis  presents 
characteristics  similar  to  this  process  of  reduction. 

The  end  of  induction  is  to  discover  a law  having  objective 
validity  and  universal  application.  There  is  a distinction 
which  must  be  noticed  and  clearly  kept  in  mind;  namely, 
the  distinction  between  a law  and  a rule.  Induction  seeks 
a law,  and  not  a rule.  A law  expresses  the  essential  and 
universal  relations  subsisting  between  given  phenomena, 
eliminating  entirely  all  accidental  and  local  coloring.  A 
law  has  objective  validity,  and  preserves  a constant  nature. 
There  can  be  only  one  law  in  reference  to  one  and  the  same 
connection  of  facts.  A rule  however  is  subjective,  dealing 
with  the  individual’s  attitude  to  phenomena,  rather  than 
an  explanation  of  the  essential  features  of  the  phenomena 
themselves.  It  often  is  determined  in  the  concrete  by  that 
which  is  external,  local,  and  accidental.  There  may  be 
many  rules,  varying  with  many  minds  and  many  tastes. 
Fundamental  and  universal  laws  of  political  economy  be- 
come maxims  and  rules  in  different  communities.  The  laws 
of  morality,  universal  and  immutable,  become  rules  of  con- 
duct in  individual  experience,  admitting  of  wide  difference 
of  opinion  and  diversity  of  application.1  In  the  processes 
of  induction,  therefore,  the  law  is  the  desideratum,  and  not 
the  rule. 

Law  however  is  used  rather  loosely  in  our  ordinary  ter- 
minology. Law  as  used  in  jurisprudence  has  a meaning 
quite  different  from  law  as  used  in  physical  science.  And 
so,  also,  the  laws  of  biology,  the  laws  of  political  economy, 
the  laws  of  ethics,  are  referred  to  with  different  shades  of 
meaning  in  each  sphere.  However  ambiguous  may  be  the 
significance  of  “ law  ” in  ordinary  thought  and  usage,  never- 
l Lotze,  Logic,  p.  335. 


ESSENTIALS  OF  INDUCTION 


181 


theless  in  induction  it  lias  a constant  and  a simple  signifi- 
cance, which,  if  carefully  adhered  to,  will  avoid  confusion 
and  obscurity  as  well,  in  our  inferential  processes  and 
results.  Law  in  induction  is  always  in  the  form  of  an 
hypothetical  universal : — 

If  A is,  B is. 

It  does  not  assert  what  has  happened,  but  what  should  hap- 
pen under  certain  conditions.  Given  the  antecedent  A,  a 
certain  determinate  consequent  B is  always  necessitated. 
The  relation  is  constant  and  invariable,  and  therefore  has  a 
universal  significance. 

Induction  holds  a peculiar  and  important  place  in  our 
everyday  life,  because  it  has  to  do  with  the  analytical 
treatment  of  instances  as  they  appear  in  experience.  The 
large  part  of  our  conscious  thinking  has  to  do  with  the  con- 
crete, the  raw  material  of  experience ; this,  induction  alone 
can  handle.  Leonardo  da  Vinci's  maxim  was  “ to  begin  with 
experience  and  by  means  of  it  to  direct  the  reason.”  1 Thus 
the  superstructure  of  knowledge  is  raised  day  by  day.  The 
given  is  continually  being  interpreted  and  referred  to  its 
appropriate  place,  as  the  stones  of  the  quarry  are  hewn  and 
fitted  into  their  proper  position  in  the  building  for  which  they 
have  been  designed.  There  are  certain  individual  experi- 
ences which  it  is  impossible  to  determine  through  our  syllo- 
gistic forms.  They  cannot  be  judged  deductively.  There 
is  no  general  category  under  which  they  can  be  subsumed. 
They  may  be  formally  illogical  if  thus  expressed,  and  yet 
admit  of  direct  investigation  and  experiment  in  the  induc- 
tive manner,  for  the  purpose  of  disclosing  the  law  under- 
lying them  and  as  yet  unknown. 

It  often  happens  that  through  indifference  or  indolence 
we  are  content  to  refer  many  phenomena  to  long-established 
and  convenient  categories,  which,  if  investigated  indepen- 
dently, we  would  find  could  not  possibly  be  so  treated.  The 
1 Ueberweg,  Logic,  p.  42. 


182 


INDUCTIVE  LOGIC 


convenient  pigeon  hole,  because  near  at  hand,  receives  much 
that  does  not  properly  belong  there.  It  is  the  office  of 
induction  to  investigate  anew  the  old  material,  and  then 
to  reclassify  in  accordance  with  the  revised  generalizations 
which  such  investigations  may  necessitate. 

The  procedure  by  induction  is  in  keeping  with  the  scien- 
tific spirit  of  the  day,  — to  interpret  the  phenomena  of 
nature  as  given,  and  not  to  anticipate  nature  through  pre- 
conceptions, and  wrest  fact  in  order  to  fit  theory.  It  comes 
to  the  sources  in  nature  with  empty  vessels,  to  draw  and 
carry  away  that  which  nature  alone  can  give. 


CHAPTER  III 


TYPES  OF  INDUCTIVE  INFERENCE 

The  process  of  induction,  as  we  have  seen,  is  a procedure 
from  given  instances  to  the  discovery  of  the  law  which 
underlies  them,  and  which  is  the  ground  of  the  connection 
of  the  various  attributes  and  relations  that  unite  in  the  one 
concrete  whole.  Viewed  from  the  standpoint  of  the  direc- 
tion of  the  process,  we  have  found  that  it  is  always  toward 
some  general  expression  of  individual  experiences,  and  in 
this  respect  it  is  the  inverse  of  deduction,  which  proceeds 
from  the  general  to  the  particulars  which  are  embraced  in  it. 
There  is  however  another  and  important  point  of  view  that 
should  not  be  overlooked.  We  have  to  consider  the  mode 
of  the  process  as  well  as  its  direction ; not  merely  the  result 
to  be  attained,  but  also  the  peculiar  manner  of  realizing  the 
same  must  be  considered.  Difference  in  method  here  gives 
rise  to  various  kinds  of  inductive  inference.  The  end  pro- 
posed in  all  is  to  generalize  our  experiences  as  they  occur 
in  the  concrete  and  particular.  When  I find  a given  phe- 
nomenon, A,  given  in  consciousness,  and  characterized  by 
several  distinctive  features  among  which  I note  specially 
the  mark  B,  the  question  at  once  most  naturally  suggests 
itself,  Is  there  a reasonable  expectation  that  I shall  always 
find  B as  an  inseparable  accompaniment  of  A,  so  that  I can 
assert  confidently  that  whenever  A is  found,  B also  will  be 
found  ? There  are  three  ways  of  satisfying  ourselves  as  to 
the  existence  of  any  constant  rather  than  coincidental  con- 
nection between  antecedent  and  consequent,  as  A and  B. 
These  give  rise  to  three  different  methods  of  inductive 
research,  and  they  are  as  follows  : — 

183 


184 


INDUCTIVE  LOGIC 


I.  The  Method  of  Enumeration. 

II.  The  Method  of  Analogy. 

III.  The  Method  of  Scientific  Analysis,  or  search  after 
causal  connection. 

Failure  to  distinguish  between  the  three  methods  has 
given  rise  to  confusion  in  the  definition  of  and  correspond- 
ing reference  to  inductive  inference ; some  authors  use 
induction  in  one,  and  some  in  another  of  these  senses.  It 
is  necessary  to  discriminate  carefully,  and  to  maintain  a 
strict  consistency  in  the  usage  of  the  terms  as  defined. 

I.  The  Method  of  Enumeration.  — We  observe  the  various 
instances  in  which  certain  attributes,  as  A and  B,  are  con- 
joined in  our  experience.  We  count  them  in  the  sense  of 
noting  to  what  extent  they  accumulate  without  noticing 
any  exception  to  what  seems  at  least  an  invariable  connection. 
We  do  not  necessarily  count  by  precise  enumeration  reaching 
a numerically  definite  result.  We  notice  merely  to  what 
extent  the  observed  instances  of  like  nature  accumulate ; 
that  is,  whether  a few,  a considerable  number,  or  a very 
large  number.  The  mere  number  of  instances  produces  a 
certain  psychological  impression,  whatever  may  be  their 
logical  force.  This  is  brought  about  through  the  laws  of 
association,  and  creates  an  expectation  of  a continuous 
repetition  of  the  experience  in  question.  This  arises  from 
a natural  tendency  of  the  mind  to  generalize.  We  observe 
that  crows  are  black  ; and  the  increasing  number  of  confirm- 
ing instances  goes  far  to  establish  a connection  between  the 
crow  and  its  color  which  seems  to  have  universal  validity. 
The  enumeration  of  instances  may  lead  us  to  any  one  of 
three  results  : — 

1.  We  may  meet  with  no  exception  whatsoever,  until  the 
scope  of  observation  completely  embraces  the  sum  of  all 
possible  instances.  This  is  complete  enumeration,  and 
when  enumeration  reaches  this  limit,  it  passes  over  into 
deductive  reasoning,  by  virtue  of  the  logical  canon  that 


TYPES  OF  INDUCTIVE  INFERENCE 


185 


whatever  is  true  of  the  parts  is  true  of  the  whole  distribu- 
tively ; that  is,  provided  the  summation  of  the  parts  has 
been  an  exhaustive  one.  We  assert  that  all  the  sheep  of  a 
given  flock  are  white ; for  we  have  observed  each  separately, 
and  no  one  has  been  missed  in  the  count.  So,  also,  the 
judgment  that  all  planets  move  around  the  sun,  resulting 
from  an  enumeration  of  the  planets  one  by  one.  It  is 
possible  also  to  have  a perfect  induction  with  an  infinite 
enumeration  of  parts.  This  is  possible  in  two  cases,  as 
pointed  out  by  Beneke.1  First,  when  the  parts  are  con- 
nected together  continuously  in  space.  This  occurs  in 
geometrical  demonstration  when  the  inference,  based  upon 
the  simple  figure  it  refers  to,  is  extended  to  all  figures  falling 
under  the  like  definition.  And  second,  when  the  parts  are 
not  continuously  connected,  if  it  can  be  proved  syllogistically 
that  what  is  true  of  a definite  ?ith  part,  must  also  be  true 
for  the  (n  -f  l)th  part. 

Perfect  induction  also  embraces  arithmetical  method  and 
computation.  Here  the  whole,  which  is  the  sum  of  the 
facts  in  each  case,  is  a totality  or  universal  whose  differences, 
which  are  all  separate  and  distinguishable,  are  yet  homo- 
geneous and  equal.2  There  is  no  qualitative  differentiation 
of  parts,  only  a quantitative  one.  The  total  is  the  sum  of 
the  units,  and  each  unit  is  like  every  other  one.  If  we 
have  one  hundred  units  making  a totality,  the  one  that  may 
be  the  twenty -seventh  is  precisely  like  the  sixty-seventh. 
It  is  a case  where  each  one  counts  for  one  and  no  one  for 
more  than  one,  in  an  absolutely  literal  sense. 

It  has  been  urged  against  perfect  induction  that  it  affords 
no  new  information,  and,  therefore,  its  results  are  not 
valuable.  However,  the  summation  of  particulars  in  abbre- 
viated forms  is  always  an  advantage.  It  is  a labor-saving 
process  to  the  mind.  It  enables  the  mind  to  retain  a large 
number  of  facts  by  throwing  them  into  one  and  the  same 

1 Quoted  by  Ueberweg,  Logic , p.  482. 

2Bosanquet,  Logic,  Vol.  II,  p.  54. 


186 


INDUCTIVE  LOGIC 


category ; and  it  facilitates  arithmetical  processes  by  conven- 
ient comprehending  of  units  within  a totality. 

2.  The  second  result  that  is  possible,  is  that,  in  counting 
instances,  our  enumeration  should  prove  incomplete.  From 
the  necessities  of  the  case,  we  are  often  not  able  to  observe 
the  entire  sphere  of  possible  occurrences  and  cover  the  whole 
ground.  It  may  be  that  beyond  the  sphere  of  our  expe- 
rience, the  constant  connection  between  certain  phenomena 
may  be  disturbed  by  the  appearance  of  some  variable  factor 
of  which  we  have  been  wholly  ignorant.  It  is  the  possibili- 
ties beyond  the  sphere  of  observation  which  render  uncertain 
the  results  of  our  count.  We  are  sure  as  far  as  we  have 
observed  ; but  we  have  not  gone  far  enough  perhaps.  Such 
results,  formulated  in  general  propositions,  are  termed 
empirical  laws ; that  is,  generalizations  from  an  experience 
necessarily  limited. 

3.  We  have  still  a third  case  ; where  in  our  enumeration 
of  positive  instances  we  meet  with  exceptions  to  a greater 
or  less  extent.  Here  we  cannot  even  sum  up  the  actual 
experience  in  terms  of  a generalization.  There  are  out- 
standing exceptions  which  will  invalidate  it.  We  must, 
therefore,  fall  back  upon  the  theory  of  probability  and  the 
calculation  of  chances,  presuming  that,  in  general,  we  will 
meet  with  the  same  proportion  of  exceptions  to  positive 
instances  in  the  future,  that  we  have  already  observed  in 
the  past.  So  we  make,  in  our  minds  at  least,  comparative 
tables  of  positive  cases  over  against  exceptions,  and  reach  a 
summary  of  the  result  in  the  form  of  a ratio,  whose  numera- 
tor will  be  the  number  of  positive  cases  observed,  and  the 
denominator  the  total  number  of  instances  including  positive 
instances  and  the  corresponding  exceptions.  We  observe 
that  some  cryptogamous  plants  possess  a purely  cellular 
structure ; others,  however,  do  not,  being  partially  vascular. 
The  probability  that  a new  cryptogam  will  be  cellular  can 
be  estimated  only  on  the  ground  of  the  comparative  number 
of  known  cryptogams  which  are  cellular,  as  over  against 


TYPES  OF  INDUCTIVE  INFERENCE 


187 


the  total  number  of  cryptogams,  both  cellular  and  vascular, 
previously  observed.1 

II.  The  Method  of  Analogy.  — Here,  also,  we  start  with 
the  experience  that  A is  characterized  by  the  mark  B. 
But  there  is  additional  knowledge  of  which  we  may  avail 
ourselves  in  the  generalization  of  some  past  experience 
already  effected,  such  as  the  following : that  A very  closely 
resembles  C,  in  that  the  two  have  many  properties  or  attri- 
butes in  common.  The  inference  by  analogy  is  that  C also, 
as  well  as  A,  will  have  the  mark  B.  It  may  be  that  we 
cannot  examine  C in  a number  of  various  instances  to  see  in 
how  many  the  mark  B occurs.  Our  only  resource  is  the 
inference  which  is  based  upon  the  known  resemblances,  or 
analogies.  This  kind  of  inference,  for  example,  was  em- 
ployed by  Sir  Isaac  Newton  in  a very  interesting  manner. 
He  had  observed  that  certain  “fat,  sulphureous,  unctious 
bodies,”  such  as  camphor,  oils,  spirit  of  turpentine,  amber, 
etc.,  have  refractive  powers  two  or  three  times  greater  than 
might  be  anticipated  from  their  densities.  He  noticed  also 
the  unusually  high  refractive  index  of  diamond,  and  from 
this  resemblance,  based  upon  similarity  in  reference  to  one 
attribute  only,  he  inferred  that  diamond  also  would  prove 
to  be  combustible.  His  prediction  in  this  regard  was  veri- 
fied by  the  Florentine  Academicians  in  1694.2  Brewster 
made  a striking  comment  upon  Newton’s  inference,  to  the 
effect  that  if  Newton  had  drawn  a like  analogy  in  refer- 
ence to  greenockite  and  octahedrite  as  he  did  concerning 
diamond,  inasmuch  as  they,  too,  have  a very  high  refrac- 
tive index,  he  would  have  been  wholly  incorrect.  This  is 
an  indication  of  the  fact  that  argument  by  analogy  is  not 
conclusive. 

Bosanquet  has  very  strikingly  expressed  the  essence  of 
the  analogical  method  in  saying  that  “in  analogy  we  weigh 
the  instances  rather  than  count  them.”3  The  distinction 

1 Jevons,  Principles  of  Science,  pp.  146,  147.  2 Ibid.  p.  527. 

3 Bosanquet,  The  Essentials  of  Logic,  p.  155. 


188 


INDUCTIVE  LOGIC 


between  analogy  and  enumeration  of  instances  lies  in  tbis, 
that  in  the  former  we  count  similar  attributes  in  the  con- 
tents of  two  instances,  and  balance  them  against  the  dis- 
similar or  unknown.  In  induction  by  enumeration  we  count 
similar  instances,  considering  them  in  their  totality  without 
examination  and  comparison  of  their  respective  attributes. 

III.  The  Method  of  Scientific  Analysis.  — The  instance  in 
question,  A,  which  is  characterized  by  the  mark  B,  is  sub- 
jected to  a vigorous  analytical  examination,  to  show  that  A 
and  B are  related  through  a causal  connection.  This  analy- 
sis is  effected  either  through  a minute  observation  or  by 
means  of  exact  experiment.  The  end  to  be  attained  by  such 
analysis  is  to  separate  a complex  phenomenon  into  its 
several  elements,  by  which  process  a causal  connection  may 
be  revealed,  whose  very  existence  is  disguised  by  the  com- 
plexity of  the  phenomenon.  For  instance,  the  phenomenon 
of  death  following  the  taking  of  arsenic  is  an  event  so  com- 
plex as  to  evade  a precise  determination  of  the  causal  rela- 
tion. When  analyzed  into  simpler  elements,  it  is  found 
that  the  immediate  effect  of  arsenic  upon  the  bodily  tissues 
is  to  harden  them  so  as  to  prevent  their  normal  functioning. 
This  is  the  causal  ground  of  the  death  due  to  arsenic. 
Moreover,  this  analytic  process,  which  may  be  appropriately 
called  a material  one,  is  supplemented  by  a formal  process 
of  negation ; that  is,  an  instance  in  which  the  suspected 
causal  element  is  absent  in  the  complex  phenomenon  under 
investigation,  and  the  related  effect,  before  observed,  now 
no  longer  appears.  This  formal  process  acts  as  a check, 
and  as  a verification  as  well,  of  the  material  analysis  of  the 
phenomenon.  For  example,  an  antidote,  as  sesquioxide  of 
iron,  being  administered,  no  death  from  arsenic  occurs ; and 
it  is  also  observed  that  no  hardening  of  the  tissues  has 
resulted,  therefore  the  former  result,  hardening  of  tissues 
producing  death,  has  been  thus  corroborated  negatively  by 
the  fact  that  where  no  hardening  of  tissues  has  resulted, 
death  does  not  follow. 


TYPES  OF  INDUCTIVE  INFERENCE 


189 


We  see  at  once  the  advantage  of  such  a method  over  that 
of  counting  all  instances  where  taking  of  arsenic  has  caused 
death.  The  latter  is  a phenomenally  adjudged  result;  the 
former  penetrates  with  analytic  insight  to  the  ground  of  the 
phenomenon  itself.  Thus  one  instance,  if  its  parts  and 
their  manifold  relations  are  adequately  comprehended,  may 
suffice  for  a universal  conclusion  based  upon  it.  It  is  true, 
however,  as  remarked  by  Bosanquet,  that  “ number  of  ob- 
servations does,  as  a rule,  assist  analysis  and  contribute  to 
eliminating  error.  Scientific  analysis  as  such,  however, 
does  not  deal  with  instances,  but  only  with  contents.” 1 

In  cases  where  the  phenomenon  does  not  reveal  its  com- 
ponent elements  under  observation,  and  it  is  impossible  to 
subject  it  to  experiment,  the  most  likely  cause  of  the  effect 
in  question  is  tentatively  judged  to  be  the  real  cause,  until 
it  can  be  verified  in  reality.  This  is  procedure  by  hypothe- 
sis, and  is  always  resorted  to  as  preliminary  to  a subsequent 
experiment  which  is  its  test,  or  else  in  lieu  of  such  an  ex- 
periment when  it  is  by  the  nature  of  the  case  precluded. 
It  is  a form  of  ideal  analysis.  The  experiment  is  constructed 
mentally.  The  phenomenon  is  separated  into  what  we  would 
reasonably  imagine  its  simpler  elements  would  be.  We  are 
constrained  to  believe  that  if  the  hypothetical  antecedent 
existed,  it  would  be  adequate  to  produce  the  effect.  Al- 
though rising  in  the  sphere  of  the  imagination,  it  is  that 
with  which  the  mind  is,  for  the  time  at  least,  satisfied  as 
an  explanation  of  the  facts  which  demand  some  cause  to 
account  for  them.  Kegarding  induction  as  a process  of 
reduction,  hypothesis  is  the  assumed  universal  or  middle 
term,  which  will  necessitate  the  phenomenon  under  investi- 
gation as  its  logical  conclusion. 

We  will  now  proceed  to  a further  examination  of  these 
methods,  considered  both  singly  and  together. 

1.  They  all  proceed  upon  the  supposition  that  what  is 
given  in  consciousness  has  some  necessary  ground  for  its 
1 Bosanquet,  Logic , Vol.  II,  p.  118. 


190 


INDUCTIVE  LOGIC 


being.  In  enumerative  induction,  there  is  some  causal  con- 
nection presupposed,  yet  in  a very  general  and  indefinite 
manner,  and  accompanied  by  no  analysis  of  the  various 
concepts  either  by  a systematic  observation  or  experiment. 
It  is  a vague  sense  of  uniformity,  which,  when  observed 
for  many  times,  we  feel  will  continue  indefinitely.  That 
which  has  happened  often  and  not  contradicted  carries 
with  it  a certain  convincing  power  by  dint  of  bare  repeti- 
tion, especially  to  persons  of  narrow  experience,  and  un- 
accustomed to  discriminating  observation.  Ueberweg  has 
made  the  following  comment  in  reference  to  the  so-called 
imperfect  induction.  “ The  conclusion  is  made  universal 
with  more  or  less  probability,  and  the  blank  which  remains 
over  in  the  given  relations  of  spheres  is  legitimately  filled 
up  partly  on  the  universal  presupposition  of  a causal-nexus 
in  the  objects  of  knowledge,  partly  on  the  particular  pre- 
supposition that  in  the  case  presented  such  a causal-nexus 
exists  as  connects  the  subject  and  predicate  of  the  conclu- 
sion. The  degree  of  probability  of  the  inductive  inference 
depends  in  each  case  on  the  admissibility  of  this  last  presup- 
position, and  the  various  inductive  operations,  the  extension 
of  the  sphere  of  observation,  the  simplification  of  the  ob- 
served conditions  by  successive  exhaustion  of  the  unessen- 
tial, etc.,  all  tend  to  secure  its  admissibility.”1 

Analogy  likewise  proceeds  upon  the  assumption  of  an 
underlying  cause  among  the  observed  phenomena,  and  this 
is  more  definitely  in  the  foreground  throughout  the  process 
than  in  that  of  induction  by  enumeration.  Analogy  is  based 
upon  the  postulate  that  similar  phenomena  have  similar 
causes ; the  greater  the  agreement  of  the  various  attributes 
of  the  different  phenomena  compared,  the  greater  will  be 
the  resultant  probability  that  causes  capable  of  producing 
them  as  effects  will  be  similar.  The  similarity  of  the  light- 
ning flash  to  the  electric  spark  suggested  to  Benjamin  Frank- 
lin the  possibility  that  they  were  due  to  a like  origin,  and 
1 Ueberweg,  Logic,  pp.  483  f. 


TYPES  OF  INDUCTIVE  INFERENCE 


191 


by  experiment  his  analogical  reasoning  was  actually  con- 
firmed, as  is  well  known.  Upon  the  theory  that  the  world 
as  it  exists  for  us  in  knowledge  forms  a system,  to  some 
place  in  which  every  phenomenon  given  in  experience  must 
be  appropriately  and  necessarily  referred,  it  follows  there- 
fore that  a simple  experience  devoid  of  any  complexity  of 
parts  may  fit  into  several  possible  places  in  our  world  of 
consciousness,  and  remain  so  far  forth  indeterminate.  How- 
ever, a complex  phenomenon,  with  many  parts  intricately 
connected,  will  fit  into  one  unique  place  only  in  the  system 
to  which  it  must  be  referred.  It  is  like  a key  that  will  fit 
into  only  one  lock.  The  presumption  therefore  is  that  any 
other  phenomenon  which  resembles  the  first  through  much 
of  its  entire  content,  part  for  part,  attribute  for  attribute, 
will  also  resemble  it  further  as  regards  other  attributes  not 
yet  examined,  so  that  it  will  likewise  fit  into  the  peculiar 
place  in  the  system  of  knowledge  to  which  the  first  has  been 
found  to  belong.  There  is  always  a strong  probability  that 
agreement  in  spheres  of  great  complexity  is  not  a mere 
coincidence,  but  the  result  of  a causal  relation.  One  charac- 
teristic of  a system,  which  we  have  found  to  be  the  ground 
of  inference  generally,  is  the  coordination  of  like  things 
under  one  concept.  Analogy  therefore  is  based  upon  the 
view  of  causal  connections  within  the  system  which  com- 
prises the  world  as  given  in  consciousness. 

In  the  third  method,  the  causal  relation  is  more  promi- 
nent still,  and  the  search  for  it  characterizes  the  procedure 
employed.  That  which  in  the  other  methods  may  exist 
merely  as  a vague  impression  is  here  formulated  and  made 
the  direct  and  sole  object  of  research. 

2.  The  three  methods  in  the  order  here  presented  show 
an  increasing  prominence  given  to  the  causal  connection  in 
the  phenomena  of  experience.  And  therefore  they  possess 
a relatively  increasing  scientific  value.  As  the  first  has 
only  indirect  reference  to  the  causal  connection  of  its  facts, 
it  is  the  least  trustworthy  and  has  no  claim  as  a scientific 


192 


INDUCTIVE  LOGIC 


method.  It  breaks  down  as  soon  as  an  exception  is  noted ; 
and  is  even  weakened  by  the  fact  that  it  is  constantly  men- 
aced by  the  possibility  at  least  of  the  appearance  of  an  ex- 
ception. “ How  do  we  know,”  says  Green,  “ that  the  instances, 
with  the  examination  of  which  we  are  always  dispensing  on 
the  strength  of  the  rule  (that  is,  our  generalization),  might 
not  be  just  what  would  invalidate  it,  if  they  were  exam- 
ined ? ” 1 We  may  arrive  at  the  conclusion,  based  upon  our 
observation  and  consequent  record,  that  all  sheep  are  white, 
and  yet  black  sheep  do  occur,  in  every  flock,  as  the  prov- 
erb has  it.  According  to  Aristotle,  the  proposition  that 
all  swans  are  white,  was  a perfectly  general  one,  and  yet  in 
recent  times  black  swans  have  been  discovered  in  Australia. 
Bacon’s  criticism  upon  this  method  has  become  classic : 
“ Inductio  quae  procedit  per  enumerationem  simplicem,  res 
puerilis  est  et  precario  concludit  et  periculo  exponitur  ab 
instantia  con  trad  ictoria  et  plerumque  secundum  pauciora 
quam  par  est  et  exiis  tantummodo  quae  presto  sunt  pro- 
nunciat.”  2 

The  validity  of  this  method  of  procedure  depends  largely 
upon  the  probability  of  our  meeting  and  noticing  exceptions 
were  they  to  occur.  As  Lotze  puts  it:  “A  man  who  never 
observes  a place  of  public  resort  but  once  in  every  seven 
days,  and  that  on  a Sunday  afternoon,  has  no  right  to  sup- 
pose, because  it  is  crowded  then,  that  it  is  as  crowded  on  a 
week-day.” 3 He  is  here  in  no  position  to  note  the  excep- 
tions even  should  they  occur. 

Analogy,  unless  confirmed  by  experiment,  or  upon  the 
ground  of  resemblance  established  by  a verifiable  hypothesis, 
has  no  claim  to  be  considered  as  a scientific  method.  There 
may  be  false  analogies  depending  upon  surface  resemblances. 
A child  might  conclude  that  oil  would  put  out  fire  because 
it  so  closely  resembles  water,  which  he  knows  can  extinguish 
the  flames.  The  difference  between  essential  and  accidental 

1 Green,  Philosophical  Works,  Vol.  II,  p.  282. 

2 Novum  Organum,  i.  105.  8 Lotze,  Logic,  p.  343. 


TYPES  OF  INDUCTIVE  INFERENCE 


193 


agreement  between  phenomena  can  be  revealed  only  when 
the  underlying  cause  is  ascertained. 

The  third  method  alone  has  scientific  worth.  True  in- 
duction must  be  a continued  search  to  discover  a causal 
relation. 

3.  The  two  first  processes  fulfil  their  functions  largely 
as  tentative  and  suggestive  methods.  In  enumeration  of 
instances,  we  are  often  led  to  note  resemblances  which 
become  the  basis  of  analogy.  And  analogy  suggests,  in 
turn,  hypothesis  which  is  capable  of  verification  through 
subsequent  experiment. 

The  question  may  be  put,  “ Which  of  the  three  processes 
is  induction  proper  ? ” The  fact  is  that  it  may  involve  all 
three,  but  it  is  not  complete  until  it  reaches  the  third,  — the 
experimental  method.  Analogy  is  especially  fertile  in  sug- 
gestion. Scientific  minds  most  carefully  trained  and  versed 
in  scientific  methods  of  research  are  often  most  keen  in 
noting  resemblances,  and  detecting  analogies  which  become 
the  basis  of  their  experiments.  Newton  possessed  that  rare 
insight  which,  in  spite  of  the  manifest  dissimilarity  of  the 
two  phenomena,  could  yet  discern  an  essential  likeness  be- 
tween the  fall  of  an  apple  and  the  gravitating  force  of  the 
moon  toward  the  earth. 

4.  It  is  also  to  be  observed  that  the  choice  of  method  will 
depend  largely  upon  mental  habit.  Some  minds  naturally 
or  by  special  training  and  surroundings  are  given  to  experi- 
ment. They  have  a testing  facility  and  inventive  capacity. 
Others  naturally  are  susceptible  in  an  unusual  degree  to 
contrasts  and  resemblances.  Others  again  are  accustomed 
to  accurate  observation  that  is  ever  pushing  beyond  and 
seeking  to  extend  its  sphere.  Thus  we  have  a natural  divi- 
sion of  these  methods  according  to  psychical  proclivities. 
The  choice  of  method  is  often  conditioned  by  the  force  of 
circumstances.  Experiment  is  not  always  possible.  Are  all 
crows  black  ? There  is  no  connection  between  the  general 
organism  of  the  crow  and  its  color  that  has  thus  far  been 


194 


INDUCTIVE  LOGIC 


revealed  through  analysis  or  experiment.  The  only  recourse 
is  to  number  instances  over  the  widest  possible  field.  We 
say,  moreover,  that  Mars  may  be  inhabited ; for  it  has  an 
atmosphere  similar  to  the  earth  and  therefore  capable 
of  sustaining  life.  Analogy  is  the  only  guide  in  such  a case, 
and  it  is  impossible  to  verify  it  either  by  observation  or 
experiment. 

5.  All  the  methods  tend  to  one  end,  that  of  effecting  a 
generalization  of  experience.  The  generalization  may  be 
either  a numerically  general  one,  or  one  expressed  in  terms 
of  a generic  concept. 

(1)  The  former  consists  in  the  extension  of  several  in- 
stances to  their  repetition  under,  like  conditions. 

(2)  The  second  consists  in  the  extension  of  several  in- 
stances to  all  cognate  species  under  the  same  genus. 

Examples  of  these  two  kinds  of  generalization  are  as 
follows : The  general  proposition  that  all  sulphur  is  com- 
bustible is  of  the  former  kind  ; all  instances  are  substantially 
of  the  same  nature,  and  do  not  differ  as  distinguishable 
species  under  the  same  genus,  but  rather  a repetition  of 
like  phenomena.  The  general  concept  in  the  above  propo- 
sition is  of  the  nature  of  an  infima  species.  On  the  other 
hand,  the  proposition  that  all  mammals  are  vertebrates,  has 
the  subject-term  in  form  of  a generic  concept.  Many  spe- 
cies, differing  widely  among  themselves,  may  be  embraced 
under  it.1 

1 Sigwart,  Logic,  Vol.  II,  pp.  310,  311. 


CHAPTER  IV 


CAUSATION 

We  have  seen  that  induction  as  a truly  scientific  method 
consists  in  the  analytical  determination  of  the  relations  of 
cause  to  effect  in  any  complex  phenomenon,  accompanied 
by  a generalization  of  the  result  obtained.  The  final  out- 
come of  such  a process  is  a universal  concept  which  em- 
bodies a law,  expressed  in  terms  of  a constant  connection 
between  antecedent  and  consequent.  As  Green  has  said, 
“ The  essence  of  induction  consists  in  the  discovery  of  the 
causes  of  phenomena.” 1 A causal  view  of  the  universe 
gives  rise  to  logical  concepts,  whereas  a mythological  view 
of  the  universe,  as  in  ancient  times,  resulted  in  mere  empiri- 
cal concepts,  which  gave  no  assurance  either  of  stability  or 
invariability.  It  will  be  necessary  therefore  to  determine 
more  precisely  the  logical  significance  of  the  causal  idea, 
which  seems  to  underlie  all  inductive  inference.  This  is  no 
easy  task.  According  to  Clifford,  “ cause  ” has  sixty-four 
meanings  in  Plato,  and  forty-eight  in  Aristotle.2 

The  causal  idea  has  sometimes  found  expression  in  the 
phrase,  the  uniformity  of  nature,  or  it  is  often  referred  to 
as  the  doctrine  of  universal  causation.  These  two  phrases 
are  often  used  interchangeably  ; this  gives  rise  to  confusion 
of  thought,  for  their  meanings  are  quite  distinct. 

Uniformity  of  nature,  strictly  interpreted,  means  that  like 
antecedents,  under  precisely  the  same  conditions,  will  be 
followed  by  like  effects ; this  idea  expresses  one  phase  of 
causation,  viz.  its  invariability. 

1 Green,  Philosophical  Works,  Vol.  I,  p.  284. 

2 Clifford,  Lectures  and  Essays,  Vol.  I,  p.  149. 

195 


196 


INDUCTIVE  LOGIC 


The  doctrine  of  universal  causation,  however,  expresses 
the  impossibility  of  phenomena  rising  spontaneously,  with- 
out an  antecedent,  or  antecedents,  sufficient  rationally  to  ac- 
count for  them.  The  two  ideas  lie  at  the  root  of  the  causal 
idea.  As  Tennyson  has  put  it : — 

For  nothing  is  that  errs  from  Law. 

Some  confusion  has  also  arisen  from  the  failure  to  discrimi- 
nate precisely  between  the  philosophical  and  the  purely 
logical  questions  relative  to  the  general  subject  of  causa- 
tion. Causation  may  be  viewed  from  three  different  points 
of  view : — 

1.  What  it  is  phenomenally,  that  is,  as  regards  its  physi- 
cal aspects. 

2.  What  it  is  essentially,  as  regards  its  real  nature.  This 
is  a metaphysical  question. 

3.  What  it  is  in  respect  to  its  characteristic  attribute  of 
invariability.  This  is  a purely  logical  question. 

(1)  As  to  the  first,  what  is  causation  phenomenally  ? 
What  is  its  purely  physical  significance  ? Investigations 
in  this  line  have  led  to  the  doctrine  of  the  conservation  of 
energy.  This  is  substantially  the  assertion  that,  in  every 
event,  no  new  energy  is  called  forth  which  did  not  exist 
before  potentially  at  least,  nor  can  any  energy  be  ultimately 
lost;  nothing  new  is  created,  — there  is  only  a change  or 
transfer  from  one  state  or  condition  to  another.  Moreover, 
the  sum  total  of  energy  in  the  universe  is  a constant  quan- 
tity ; it  can  neither  be  added  to,  nor  subtracted  from.  There 
is  an  excellent  illustration  of  this  theory  in  the  admirable 
chapter  on  “ Conservation  of  Energy  ” by  Professor  Tait. 
I give  it  somewhat  in  full : “ I allow  an  electric  current  to 
pass  through  a galvanic  battery,  and  there  is  for  the  moment 
a certain  quantity  of  zinc  consumed,  or,  as  we  may  put  it,  a 
certain  quantity  of  potential  energy  in  the  battery  has  been 
converted  into  the  kinetic  energy  of  a current  of  electricity. 
That  current  of  electricity  passes  round  some  yards  of  cop- 


CAUSATION 


197 


per  wire,  coiled  round  a bar  of  iron  or  a number  of  fine  iron 
wires  which  are  standing  vertically  inside  this  apparatus. 
The  moment  the  current  passes,  these  iron  wires  are  con- 
verted into  magnets,  but,  in  consequence  of  the  conservation 
of  energy,  while  this  is  going  on  they  weaken  the  current. 
The  current  of  electricity  becomes  weaker  in  the  act  of 
making  the  magnet,  but  the  moment  the  magnet  springs 
into  existence,  it  again  is  weakened,  because,  from  the 
necessities  of  its  position,  its  mere  coming  into  existence 
necessitates  the  passage  of  a new  current  of  electricity  in 
another  coil  of  wire  which  surrounds  this  externally,  and 
finally  this  last  current  we  can  use  to  produce  heat,  or  light, 
or  sound.” 1 In  this  cycle  of  changes  we  see  how  closely 
connected  even  disparate  phenomena  are,  and  how  the  ap- 
pearance of  energy  in  any  one  definite  state  is  dependent 
upon  its  previous  existence  in  some  other  state.  The 
doctrine  of  conservation  of  energy,  we  shall  see  later  on, 
may  be  suggestive  as  to  the  nature  of  the  analytical  treat- 
ment of  cause  and  effect. 

(2)  The  philosophical  question  as  to  the  inner  nature  of 
causation  met  with  one  answer  generally  until  the  time  of 
Hume ; namely,  that  the  idea  of  cause  signified  that  the 
antecedent  was  efficient  in  producing  the  corresponding 
consequent,  implying  the  transfer  of  power  sufficient  to 
bring  about  the  effect.  Hume,  however,  contended  that  in  the 
greatest  possible  extent  of  our  knowledge,  all  that  we  cer- 
tainly know  is  this,  that  one  event  follows  another.  We  have 
no  ground  for  an  assertion  concerning  the  manner  in  which 
the  sequence  is  effected,  nor  for  assuming  any  real  tie  be- 
tween them.  Hume  insisted  that  phenomena  were  conjoined, 
but  never  connected.2  His  opponents,  as  Kant  and  others, 
deny  him,  however,  his  fundamental  position,  — that  the 
origin  of  the  causal  concept  comes  from  experience  alone. 
They  urged  that  it  has  an  a priori  origin,  a concept  simple 


1 Tait,  Recent  Advances  in  Physical  Science,  pp.  76,  77. 

2 Hume,  Essay  on  Idea  of  Necessary  Causation. 


198 


INDUCTIVE  LOGIC 


and  unanalyzable,  given  through  intuitive  insight;  developed 
in  the  sphere  of  experience,  but  not  dependent  upon  expe- 
rience for  its  warrant.  It  is  an  interesting  fact  that  the 
idea  of  the  conservation  of  energy  developed  subsequent 
to  Hume’s  time.  It  seems  to  give  evidence  which  Hume 
insisted  was  not  and  could  not  be  forthcoming ; namely, 
concerning  the  idea  of  the  antecedent  as  an  efficient  power. 
Through  the  modern  doctrine,  the  impression  of  a transfer 
of  real  power  is  produced,  though  its  mode  and  manner  still 
remain  a mystery. 

(3)  The  logical  aspect  concerns  not  the  phenomenal 
manifestation  of  cause  and  effect,  nor  their  inner  nature, 
but  rather  the  element  of  invariability  in  causation.  Two 
questions  here  suggest  themselves : First,  Is  invariability  a 
fact,  — a constant  element  in  causation?  Second,  How  do 
we  account  for  its  existence  ? The  first  only  has  truly 
logical  significance.  The  invariability  of  causation,  that 
like  antecedents  under  precisely  the  same  conditions  pro- 
duce like  effects,  alone  makes  induction  possible.  Mill  says 
that  it  is  the  belief  in  the  uniformity  of  nature  which  stands 
as  the  ultimate  major  premise  in  every  process  of  induction. 
Hume  accepted  it,  and  based  inferences  upon  it,  and  never 
challenged  it  as  a working  basis  as  regards  the  affairs  of 
everyday  life.  He  acknowledged  the  element  of  invaria- 
bility, and  only  denied  the  bond  of  connection.  This  ele- 
ment has  peculiar  logical  significance  : without  it,  it  would 
be  impossible  to  extend  our  knowledge  beyond  the  seen  and 
the  heard,  indeed  that  which  is  seen  and  heard  would  then 
have  no  meaning,  and  no  basis  for  their  interpretation  and 
appreciation.  Being  assumed,  however,  as  a logical  postu- 
late, we  have  a basis  for  induction,  — a constant  to  be  sought 
for  and  to  be  depended  upon,  in  explanation  of  the  past  and 
in  prediction  of  the  future. 

When  we  come  to  the  second  question,  which  is  essen- 
tially a genetic  one,  how  the  belief  in  the  uniformity  of 
nature  arose,  we  find  two  classes  which  answer  respectively 


CAUSATION 


199 


that  the  belief  arose  a priori,  and  on  the  other  hand,  from 
experience  simply.  The  former  is  the  opinion  especially 
associated  with  the  Scottish  School  of  philosophy.  Hume 
holds  that  it  proceeds  from  a psychological  law  of  custom 
or  habit,  — an  unbroken  line  of  mental  associations  induc- 
ing a belief  within,  concerning  the  uniformity  of  nature 
without.  Mill  has  also  a like  empirical  basis  for  a belief 
in  the  uniformity  of  nature  ; he  holds  that  having  observed 
uniformity  in  many  experiences,  in  fact  never  contradicted, 
we  generalize  so  as  to  cover  a sphere  beyond  our  experience. 
Moreover,  we  possess  the  consensus  of  testimony,  coexten- 
sive with  the  history  of  humanity,  of  the  indefinitely  wide 
extent  of  the  sphere  of  causation,  and  the  accompanying 
characteristic  of  uniformity.  His  position  is  fortified  by 
the  fact  that  in  the  process  of  incomplete  induction,  its 
probability  is  strengthened  where  there  has  been  exception- 
ally abundant  scope  for  observation,  so  that  there  is  the 
overwhelming  conviction  that  if  there  had  been  a time  or 
place  where  the  law  would  prove  untrue,  it  would  have  been 
noticed.  Instead  of  universal  causation,  Mill  and  his  fol- 
lowers make  a more  cautious  statement,  — causation  as 
coextensive  with  the  sum  total  of  human  experience.  This 
is  abundantly  adequate  to  embrace  all  possible  circum- 
stances of  practical  inference.  The  immensely  high  degree 
of  probability  engenders  a subjective  certitude  which  in 
everyday  conduct  of  affairs,  and  even  in  the  more  exact 
requirements  of  scientific  investigation,  is  never  questioned. 

Preyer  has  given  an  interesting  account  of  the  extremely 
early  appearance  of  the  appreciation  of  the  causal  relation 
in  the  case  of  his  child,  “who,  at  the  three  hundred  nine- 
teenth day  of  its  life,  struck  several  times  with  a spoon 
upon  a plate.  It  happened  accidentally,  while  he  was  doing 
this,  that  he  touched  the  plate  with  the  hand  that  was  free  ; 
the  sound  was  dulled,  and  the  child  noticed  the  difference. 
He  now  took  the  spoon  in  the  other  hand,  struck  with  it  on 
the  plate  and  dulled  the  sound  again,  and  so  on.  In  the 


200 


INDUCTIVE  LOGIC 


evening  the  experiment  was  renewed  with  a like  result. 
Evidently  the  function  of  causality  had  emerged  in  some 
strength,  for  it  prompted  the  experiment.  The  cause  of  the 
dulling  of  the  sound  by  the  hand  — was  it  in  the  hand  or  in 
the  plate  ? The  other  hand  had  the  same  dulling  effect,  so 
the  cause  was  not  lodged  with  the  one  hand.  Pretty  nearly 
in  this  fashion  the  child  must  have  interpreted  his  sound- 
impression,  and  this  at  a time  when  he  did  not  know  a single 
word  of  his  later  language.” 1 

The  theoretical  soundness  of  Mill’s  speculations,  however, 
has  a flaw,  although  the  practical  results  may  not  be  thereby 
invalidated.  The  inductive  process,  which  is  supposed  to 
be  a truly  scientific  method,  and  superior  to  induction  by 
simple  enumeration  must,  according  to  Mill,  at  the  last 
analysis,  rest  upon  a principle  which  is  itself  based  upon  an 
incomplete  induction.  A very  fair  and  searching  criticism 
of  Mill  is  that  of  Venn’s  in  his  Empirical  Logic.2  Whately 
insists  that  the  whole  question  concerning  the  nature  of  our 
belief  in  uniformity  is  irrelevant,  as  it  is  a purely  psycho- 
logical and  not  a logical  one.  Mansel  holds  a mediating 
position  in  insisting  that  the  idea  of  universal  causation  is 
intuitive,  while  that  of  uniformity  is  necessarily  empirical. 
Sigwart  has  very  trenchantly  criticised  Mill  in  that  “ taking 
away  with  one  hand  what  he  gives  with  the  other,  he  shows 
in  the  uncertainty  of  his  views  the  helplessness  of  pure 
empiricism,  the  impossibility  of  erecting  an  edifice  of  uni- 
versal propositions  on  the  sand-heap  of  shifting  and  isolated 
facts,  or,  more  accurately,  sensations;  the  endeavor  to  ex- 
tract any  necessity  from  a mere  sum  of  facts  must  be  fruit- 
less. The  only  true  point  in  the  whole  treatment  is  one  in 
which  Mill  as  a logician  gets  the  better  of  Mill  as  an 
empiricist;  namely,  that  every  inductive  inference  contains 
a universal  principle ; that  if  it  is  to  be  an  inference  and 
not  merely  an  association  of  only  subjective  validity,  the 

1 Preyer,  The  Senses  and  the  Will,  pp.  87,  88. 

2 Venn,  Empirical  Logic,  p.  130. 


CAUSATION 


201 


transition  from  the  empirically  universal  judgment  All 
known  J.’s  are  B to  the  unconditionally  universal  All  that 
is  A is  B,  can  only  be  made  by  means  of  a universal  major 
premise,  and  that  only  upon  condition  of  this  being  true 
are  we  justified  in  inferring  from  the  particular  known  A’s 
to  the  still  unknown  A’ s.” 1 

The  whole  tendency  of  the  modern  logic  is  to  base  the 
causal  postulate  upon  a ground  which  is  epistemological ; 
namely,  inasmuch  as  our  knowledge  is  one  and  self-con- 
sistent throughout  all  its  separate  elements,  there  must  be 
a corresponding  invariability  in  the  phenomena  themselves, 
as  there  is  in  the  system  of  knowledge  which  results  from 
the  interpretation  of  these  phenomena.  This  is  the  general 
view  of  Sigwart,  Bosanquet,  Lotze,  and  Green.2 

This  view  may  be  considered  also  as  an  expression  of  the 
Law  of  Sufficient  Reason ; namely,  that  there  is  an  inherent 
characteristic  of  intelligence  which  demands  that  every 
element  of  consciousness  must  be  referred  to  some  other 
element  for  its  explanation,  and  that  it  is  only  when  the 
logical  connection  of  ideas  corresponds  to  a real  causal  con- 
nection, that  the  mind  discovers  a reason  for  its  several 
experiences  which  is  satisfying.  It  has  been  said  by  Ueber- 
weg,  as  giving  expression  to  this  view : “ The  external  in- 
variable connection  among  sense  phenomena  is,  with  logical 
correctness,  explained  by  an  inner  conform  ability  to  law, 
according  to  the  analogy  of  the  causal  connection  perceived 
in  ourselves  between  volition  and  its  actual  accomplishment.” 3 

There  is  a distinction  that  is  of  importance  to  note  be- 
tween the  popular  and  the  scientific  idea  of  cause.  The 
former  is  the  outcome  of  the  supposition  that  whatever 
immediately  precedes  the  effect  has  evidently  produced  it, 
and  that  this  is  sufficient  wholly  to  account  for  it.  Such 

1 Sigwart,  Logic, ~V ol.  II,  p.  303. 

2 Ibid.,  Vol.  II,  pp.  119,  120  ; Bosanquet,  Logic,  Vol.  II,  pp.  220  , 251: 
Lotze,  Logic,  p.  68;  Green,  Philosophical  Works,  Vol.  II,  p.  286. 

3 Ueberweg,  Logic,  pp.  281,  282. 


202 


INDUCTIVE  LOGIC 


an  idea  of  causes  leads,  at  the  best,  but  to  a loose  and  super- 
ficial determination  of  the  relation  between  any  antecedent 
and  its  consequent,  and  there  is  the  danger,  moreover,  of  a 
hasty  inference  which  results  in  the  fallacy  of  post  hoc  ergo 
propter  hoc.  In  order  to  attain  a true  view  of  causation,  we 
must  especially  attend  to  the  extreme  complexity  of  the 
causal  connection.  There  is  no  such  thing  as  a simple 
cause  followed  by  a simple  effect.  The  cause  is  always  a 
combination  of  several  elements,  circumstances,  and  condi- 
tions ; the  effect  is  always  manifold.  This  characteristic 
has  been  admirably  presented  in  Mill’s  chapter  on  the 
“Plurality  of  Causes  and  the  Intermixture  of  Effects.”1  It 
is  well  known  that  the  variation  in  the  height  of  a barometer 
is  due  partly  to  the  variation  of  the  atmospheric  pressure, 
and  partly  to  the  variation  of  the  expansion  of  the  mercu- 
rial column  due  to  heat.  In  exact  determination,  some 
experiment  or  calculation  must  precede,  before  there  can  be 
a discrimination  between  the  elements  of  the  joint  effect. 
And  so  also,  a number  of  circumstances  may  combine  to 
restore  an  invalid  to  health,  no  one  of  which  alone  being 
capable  of  effecting  his  recovery. 

The  cause  of  any  phenomenon  has  been  defined  by  Mill, 
as  also  by  Brown  and  Herschel,  as  the  sum  total  of  all  its 
antecedents.  This  statement  has  been  criticised,  inasmuch 
as  the  sum  total  of  all  antecedents  is  indeterminate,  and 
that  there  is  no  end  to  the  possible  ramifications  in  all 
directions  which  an  exhaustive  analysis  of  any  complex 
cause  will- yield.  However,  the  problem  is  one  of  reduction 
to  simplest  possible  terms  within  the  range  of  our  powers  of 
observation  and  experiment.  There  is  much  in  the  sum 
total  of  all  the  antecedents  of  any  given  effect  which  is 
irrelevant.  It  is  the  peculiar  function  of  logical  analysis  to 
discriminate  between  the  relevant  and  irrelevant.  The 
temperature  of  the  laboratory  will  not  affect,  one  way  or 
the  other,  experiments  with  falling  bodies ; but  will  essen- 
1 Mill,  Logic,  Book  III,  Chap.  X. 


CAUSATION 


203 


tially  influence  certain  chemical  experiments,  and  must 
enter  as  one  of  the  determining  factors  in  the  sum  total  of 
antecedents.  It  may  be  that  certain  elements  of  a complex 
whole  may  seem  to  us  ultimate  and  unanalyzable,  and  yet  be 
themselves  systems  of  more  or  less  complexity.  There  is 
always  a limit  to  analysis,  both  experimental  and  mental. 
The  analysis  is  to  extend  to  the  ultimate  parts  as  far  as 
possible.  It  is  not  an  exact  process,  but  a process  which 
tends  to  exactness  to  the  extent  which  the  scope  of  finite 
intelligence  will  permit.  The  reason  is  not  at  fault  so  much 
as  the  natural  limitations  of  observation  and  experimental 
analysis.  The  end  of  our  research  in  causal  analysis  is  to 
discover  an  invariable  relation  that  can  be  expressed  in  the 
form  of  an  hypothetical  universal,  — If  A,  then  B. 

In  order  to  effect  this,  the  complex  A must  be  separated 
into  its  parts,  a,  b,  c,  etc.,  and  the  effective,  and  necessary, 
and  indispensable  element  producing  B must  be  determined. 
Suppose  it  proves  to  be  a,  it  may  be  possible  to  subject  this 
to  further  analysis,  and  to  reduce  it  to  simpler  elements,  such 
as  x,  y,  z,  etc.,  and  x be  found  as  the  significant  element  of 
the  real  cause.  Each  analysis  determines  a narrower  and 
still  narrower  sphere  within  which  the  cause  lies.  A man 
is  shot.  We  say  the  bullet  killed  him ; then  the  driving 
force  behind  the  bullet;  then  the  explosive  power  of  the 
gunpowder ; this  in  turn  was  occasioned  by  the  combined 
chemical  and  mechanical  energy  of  its  ingredients  whereby 
a solid  is  transformed  into  a gaseous  substance  many  times 
its  original  bulk. 

Sooner  or  later  we  must  reach  the  end  of  our  analysis, 
and  the  investigation  be  necessarily  checked.  No  explana- 
tion is  ultimate  ; we  only  transfer  our  point  of  view  from  a 
less  to  a more  familiar  sphere  of  interpretation.  We  do  not 
feel  the  need  of  explaining  the  very  familiar ; though  the 
most  familiar  is  hardest  satisfactorily  to  explain,  because 
there  is  nothing  simpler  in  whose  terms  we  may  paraphrase 
it.  We  feel  this  in  giving  a definition  of  terms  whose 


204 


INDUCTIVE  LOGIC 


meaning  we  best  know,  and  which  we  most  frequently  use. 
Mr.  Barrett,  a former  assistant  at  the  Boyal  Institution, 
said  of  Faraday : “ I well  remember  one  day  when  Mr. 
Faraday  was  by  my  side,  I happened  to  be  steadying,  by 
means  of  a magnet,  the  motion  of  a magnetic  needle  under 
a glass  shade.  Mr.  Faraday  suddenly  looked  most  impres- 
sively and  earnestly,  as  he  said : ‘ How  wonderful  and 
mysterious  is  that  power  you  have  there  ! The  more  I think 
over  it,  the  less  I seem  to  know.’  And  yet,  he  who  said 
this  knew  more  of  it  than  any  living  man.”  1 

Although  our  knowledge  is  limited  as  in  all  cases  of 
causation  however  simple,  nevertheless,  as  far  as  it  goes, 
the  several  elements  are  related  logically,  that  is,  necessarily 
and  universally.  We  may  only  know  in  part,  but  still  we 
know,  and  the  world,  as  interpreted  for  us  in  knowledge,  is 
a world  of  invariable  sequences.  The  process  of  inductive 
analysis,  therefore,  consists  in  reducing  a complex  antecedent 
to  its  ultimate  parts,  in  order  to  reveal  the  element  or  ele- 
ments in  it  which  may  have  caused  the  given  effect.  It  some- 
times happens  that  different  elements  in  an  antecedent  may 
be  considered  severally  as  the  cause,  according  to  the  psycho- 
logical point  of  view  as  regards  the  interests  of  the  investiga- 
tor. It  is  not  always  that  a scientific  determination  of  the 
cause  is  required ; it  may  be  that  all  that  is  desired  is  a 
knowledge  of  that  part  of  the  antecedent  which  is  most 
closely  and  prominently  connected  with  the  event  in 
question.  An  inquiry  may  be  started  in  reference  to  the 
cause  of  an  epidemic  in  a community.  One  may  discover 
the  cause  in  the  carelessness  of  sanitary  engineers ; another 
may  say  the  cause  lies  in  the  poor  construction  of  the 
sewerage  ; another  says  that  the  cause  of  the  epidemic  is  a 
certain  kind  of  bacilli.  Each  one  is  looking  at  the  chain  of 
events  related  as  cause  and  effect ; but  they  all  look  at 
different  links  of  the  same  chain.  One  element,  therefore, 
of  a complex  antecedent  may  be  brought  into  more  or  less 
1 Gladstone,  Michael  Faraday,  p.  180. 


CAUSATION 


205 


prominence  as  the  efficient  element  of  the  cause,  according 
as  the  point  of  view  is  shifted.  If,  in  the  search  for  the 
cause  of  phenomena,  the  sum  total  of  antecedents  were 
always  given  exhaustively,  the  explanation  might  become 
so  loaded  down  with  details  as  to  burden  the  mind,  and 
confuse  rather  than  clear  the  understanding. 


CHAPTER  V 


THE  METHOD  OF  CAUSAL  ANALYSIS  AND 
DETERMINATION 

It  will  be  well  to  consider  the  various  cases  which  will 
confront  us  in  seeking  to  analyze  a complex  antecedent  for 
the  purpose  of  discovering  its  cause. 

1.  There  are  instances  where  cause  and  effect  appear  in 
evident  sequence.  There  is  an  antecedent  which  is  fol- 
lowed by  a consequent.  If  A happens,  then  B will  happen. 
Instances  of  this  kind  most  readily  yield  themselves  to  the 
process  of  analysis,  because  a change  in  any  given  phenom- 
enon is  occasioned  by  the  efficiency  of  the  antecedent  which 
may  be  observed  in  connection  with  the  change  itself.  It 
is  easier  to  note  active  than  passive  relations,  the  dynamic 
rather  than  the  static.  The  attention  is  attracted  and  held 
by  change.  The  bird  flying  across  our  path  is  observed, 
and  the  one  perched  upon  the  tree  near  at  hand,  however 
conspicuous  may  be  its  position,  is  passed  by  without  any 
notice  taken  of  it.  It  is  easier  to  connect  the  moisture  of 
the  grass  with  falling  rain,  than  when  the  same  is  occa- 
sioned by  the  dew.  In  one  case,  the  causal  relation  is  ex- 
hibited in  operation ; in  the  other,  the  connection  is  veiled. 
We  find  the  grass  wet;  what  preceded  it  we  are  not  able  to 
see.  There  are  several  instances  of  sequence  among  ob- 
served phenomena  which  must  be  carefully  discriminated 
in  order  to  avoid  confusion  of  thought.  They  are  as 
follows  : — 

(1)  When  we  have  A followed  by  B,  and  A ceases  wholly 
while  B endures  for  an  appreciable  time  afterwards,  or  it 
may  be  permanently.  A billiard  ball  strikes  another,  the 

206 


CAUSAL  ANALYSIS  AND  DETERMINATION  207 


second  goes  on  by  virtue  of  the  newly  acquired  energy 
transferred  by  impact  from  the  first,  which,  however,  stops 
altogether.  I throw  a ball  which  lodges  on  the  top  of  a 
building;  the  effect  produced  lasts  permanently,  for  the 
ball  has  gained  a gravity  potential  due  to  the  energy  im- 
parted to  it  by  the  initial  throwing.  The  old  formula, 
therefore,  does  not  always  hold : “ Cessante  causa  cessat 
effectus.” 

(2)  Cases  where  A ceases,  and  thereupon  B immediately 
ceases  also.  If  we  cut  off  the  supply  of  gas  which  feeds 
a flame,  the  flame  at  once  disappears.  There  are  cases, 
however,  when  an  appreciable  time  must  elapse  in  order 
that  the  transferred  energy  in  the  effect  may  be  dissipated. 
When  we  shut  our  eyes  the  stimulus  causing  the  percep- 
tion is  cut  off,  and  the  perception  at  once  is  at  an  end; 
however,  there  are  cases  where  the  stimulus  being  very 
strong,  after-images  are  induced  which  remain  for  some 
time  in  the  dark  field  after  the  eyes  are  closed. 

(3)  Cases  where  the  antecedent  is  wholly  inadequate  to 
produce  the  effect,  but  whose  function  is  merely  to  liberate 
potential  energy  already  stored,  and  waiting  an  occasion 
for  its  active  manifestation.  A slight  blow  upon  a piece 
of  dynamite  causes  an  explosion  wholly  disproportionate 
to  the  striking  force  employed.  As  is  well  known,  heat  is 
often  an  exciting  cause  of  chemical  action.  In  such  cases 
the  real  cause  is  more  or  less  concealed,  while  that  which 
is  apparent  upon  the  surface  is  not  a cause  so  much  as  an 
occasion  of  the  phenomenon  in  question.  I touch  the  pen- 
dulum and  a clock  starts  and  so  continues  for  many  hours ; 
the  swinging  pendulum,  however,  is  only  the  occasion  of 
liberating  the  potential  energy  of  the  wound-up  spring, 
and  thence  the  power  which  runs  the  clock,  pendulum, 
wheels,  hands,  and  all. 

2.  We  have  also  instances  not  so  much  of  sequence  as 
of  concurrence.  The  planets  revolve  around  the  central 
sun;  here  the  cause  is  constant,  attended  by  constant 


208 


INDUCTIVE  LOGIC 


effect.  The  machine  never  runs  down,  nor  has  to  be 
wound  up. 

3.  Again  there  are  instances  of  coexistence.  These  are 
more  difficult  to  analyze,  for  the  phenomena  do  not  here 
appear  as  antecedent  and  consequent  in  the  midst  of  chang- 
ing conditions  and  circumstances.  We  have  coexistence 
of  two  kinds  : — 

(1)  Coexisting  attributes  in  one  and  the  same  organism. 
They  are  always  found  together.  They  form  one  generic 
concept  and  are  called  by  one  name.  Cows  have  horns, 
cloven  feet,  are  ruminant,  etc.  Dogs  have  their  distinct 
and  constant  characteristics.  The  orange  has  its  correla- 
tion of  color,  taste,  smell.  And  so  we  have  the  so-called 
“ natural  kinds,”  i.e.  organisms  presenting  an  unique  and 
characteristic  appearance,  differentiated  thereby  from  all 
others.  There  are  also  certain  correlations  of  growth  which 
present  a constant  relation  between  certain  attributes,  as 
the  fact,  however  we  may  explain  it,  that  cats  with  blue 
eyes  are  invariably  deaf.  There  are,  moreover,  illustrations 
of  the  same  in  an  inorganic  sphere,  as  the  law  which  con- 
nects the  atomic  weight  of  substances  and  their  specific 
heat  by  an  inverse  proportion;  or  that  other  law  which 
obtains  between  the  specific  gravity  of  substances  in  the 
gaseous  state,  and  their  atomic  weights,  they  being  either 
equal  or  the  one  a multiple  of  the  other.  In  many  cases, 
the  bare  fact  of  coexistence  must  be  accepted  without  being 
able  to  explain  the  causal  ground  of  it.  The  several  ele- 
ments present  a constant  association,  and  that  is  all  that 
can  be  said  about  it.  In  other  cases,  however,  a cause  may 
be  found,  for  instance,  as  regards  the  correlation  of  warm- 
blooded animals  always  possessing  lungs ; the  connection 
between  respiration  and  the  generation  of  heat  is  found  to 
depend  upon  chemical  action  as  its  causal  basis. 

(2)  A relation  of  statics  rather  than  dynamics,  as,  for 
instance,  a pillar  supporting  a roof  or  arch  is  said  to  be  the 
cause,  in  the  sense  of  the  sustaining  cause,  of  the  super- 


CAUSAL  ANALYSIS  AND  DETERMINATION  209 


structure.  So  also  the  cohesive  force  which  holds  together 
the  particles  of  a stone.  In  such  cases  the  energy  inherent 
in  the  cause  is  of  the  nature  of  a stress  and  strain. 

4.  Under  this  head  are  embraced  the  phenomena  of  vital 
growth  or  development,.  These  are  the  most  difficult  of  all 
the  causal  problems  to  determine ; for  it  is  required  to  dis- 
cover the  inner  necessity  of  essence,  and  how  the  succeeding 
stages  of  development  unfold  through  the  play  of  the  cen- 
tral forces  inherent  in  the  very  nature  and  being  of  the 
organism  itself.  Mill  is  content  with  classifying  organisms 
as  different  natural  kinds,  and  he  is  not  concerned  with  the 
reason  why  there  should  be  such  and  such  kinds,  nor  does 
he  attempt  to  discover  any  law  concerning  these  natural 
correlations  and  the  mode  of  their  growth.  In  inductive 
analysis,  our  concepts  must  not  merely  grasp  what  the  natu- 
ral kinds  are,  but  also  what  has  determined  them  to  be  what 
they  are.  Darwin  puts  special  emphasis  upon  the  environ- 
ment as  affecting  changes  in  organisms  and  producing  dif- 
ferentiating modifications  among  species.  This,  however, 
must  be  considered  not  as  sole  factor,  but  one  which  is  com- 
bined with  inner  needs  and  necessities.  Moreover,  Darwin 
has  drawn  attention  to  the  fact  that  individual  differences 
need  scientific  explanation  as  well  as  the  common  attributes, 
as,  for  instance,  why  some  sheep  are  black,  and  why  some 
pigeons  are  fantailed  and  others  are  not.  In  all  such  con- 
siderations we  must  not  lose  sight  of  the  fact  that  there  are 
two  determining  factors,  — the  inner  necessity  of  develop- 
ment, and  the  external  necessity  of  causality,  as  organisms 
are  acted  upon  by  their  environment.1 

5.  Cases  of  collocation  where  no  one  element  of  the  cause 
is  efficient,  but  together  they  all  combine  to  produce  the 
effect.  In  searching  for  the  cause,  we  must  not  only  find  a 
certain  amount  of  energy  capable  of  producing  the  effect, 
but  we  must  also  discover  what  peculiar  arrangement  of  the 
elements  concerned  must  exist  before  the  energy  in  question 

1 Sigwart,  Logic,  Vol.  II,  pp.  322,  330,  331. 


210 


INDUCTIVE  LOGIC 


can  become  operative.  Chalmers  says  that  “ the  existing 
collocations  of  the  material  world  are  as  important  as  the 
laws  which  the  objects  obey,  that  many  overlook  this  dis- 
tinction and  forget  that  mere  laws  without  collocations 
would  have  afforded  no  security  against  a turbid  and  dis- 
orderly chaos. 1 We  would  naturally  say  that  the  sole 
cause  of  water  boiling  at  212°  is  the  enveloping  heat ; it  has, 
however,  been  observed  that  on  top  of  Mont  Blanc,  water 
boils  at  180°  instead  of  212°.  This  indicates  that,  in  addi- 
tion to  the  fire,  the  atmospheric  pressure  is  an  element  in 
the  cause,  very  easily  overlooked.  Charcoal  and  diamond 
are  of  the  same  substance ; a difference  only  in  the  arrange- 
ment of  the  molecules  results  in  such  radically  different 
combinations.  There  are,  in  the  main,  three  special  kinds 
of  collocations,  as  follows  : — 

(1)  Cases  of  modifying  circumstance.  A strong  wind 
blows  down  a tree;  this  would  not  have  occurred  had  not 
the  tree  been  hollow.  The  hollowness  of  the  tree  is  here  a 
cooperative  circumstance  that  is  combined  with  the  efficient 
cause,  — the  force  of  the  wind.  An  instance  where  arrange- 
ment of  the  elements  concerned  rather  than  their  efficient 
energies  is  productive  of  the  effect,  is  that  of  capillarity,  the 
rising  of  liquid  in  a tube  of  exceedingly  small  bore.  Here 
form  is  more  essential  to  the  effect  than  the  expenditure  of 
any  visible  energy. 

(2)  Cases  in  which  certain  negative  conditions  prevent 
the  realization  of  the  effect.  The  plants  and  shrubs  die  in 
a long  drouth,  because  it  does  not  rain.  A train  collides 
with  another,  because  the  red  signal  was  not  exposed  as  it 
should  have  been.  A match  will  ignite  gunpowder  gener- 
ally, but  it  fails  to  do  so  should  the  powder  prove  to  be 
wet. 

(3)  There  are  also  cases  of  counteracting  causes,  where 
the  effect  of  cause  A is  not  realized,  as  cause  B neutralizes 
the  force  of  cause  A;  as  when  an  anchored  boat  will  not 

1 Quoted  by  Jevons,  Principles  of  Science,  p.  740. 


CAUSAL  ANALYSIS  AND  DETERMINATION  211 


respond  to  the  pull  of  the  oar.  Sometimes  the  cause  is  not 
wholly  counteracted,  or  it  may  be  the  counteracting  cause 
more  than  holds  the  positive  cause  in  check,  and  is  itself 
operative.  The  rise  of  a balloon  in  the  air  is  due  to  the  fact 
that  the  force  of  gravity  is  more  than  overbalanced  by  the 
expansive  force  of  the  gas  within  the  balloon  ; one  force  pull- 
ing downwards,  the  other  bearing  up,  and  the  latter  pre- 
vailing. 

Mechanical  forces  acting  in  combination  admit  of  a reso- 
lution of  their  joint  effect  according  to  the  theory  of  the 
parallelogram  of  forces.  Chemical  and  vital  forces  cannot 
be  treated  in  such  a way  at  all.  From  the  character  of  the 
elementary  forces  in  mechanics,  one  can  calculate  their  com- 
bination. In  chemistry,  however,  when  the  elements  are 
given,  the  resulting  compound  cannot  be  thus  determined. 
So,  also,  in  vital  and  mental  phenomena,  the  necessarily  com- 
plex nature  of  the  elements  involved  prevents  not  only 
prediction  of  resulting  combinations,  but  even  adequate 
explanation  of  that  which  may  be  immediately  given  in 
consciousness. 

It  is  necessary,  in  connection  with  these  various  instances 
of  causal  relations,  to  understand  the  different  modes  of  the 
transfer  of  energy,  which  are  as  follows  : — 

(1)  Molar  or  mechanical,  as  in  the  case  of  a billiard-ball 
transferring  its  energy  to  another  through  impact. 

(2)  Molecular,  as  heat,  chemical  and  electrical  and  mag- 
netic forces,  light,  etc.  One  passes  into  another,  as  chemical 
force  producing  electric,  electric  producing  magnetic,  or 
producing  heat  and  light. 

(3)  Cases  where  mechanical  force  becomes  molecular,  as 
friction  inducing  heat;  or  cases  where  molecular  becomes 
mechanical,  as  heat  transferred  into  the  driving  power  of  an 
engine,  or  electricity  applied  as  a motor.  A precise  deter- 
mination of  equivalents  can  be  made  between  molar  and 
molecular  energy;  as,  for  example,  it  has  been  found  that 
it  takes  the  same  amount  of  energy  to  raise  772  pounds  a 


212 


INDUCTIVE  LOGIC 


distance  of  one  foot  that  it  does  to  raise  the  temperature  of 
one  pound  of  water  1°  F. ; or  the  heat  requisite  to  boil  a 
gallon  of  freezing  water  would  lift  1,389,600  pounds  through 
a distance  of  one  foot. 

As  a consequence  of  the  doctrine  of  the  transfer  of  energy, 
a causal  law  can  be  so  stated  as  to  express  the  fact  that 
_J  variations  in  the  antecedents  will  call  for  the  corresponding 
variations  in  the  effect,  as,  for  instance,  such  a law  as  the 
following:  “Resistance  in  a wire  of  constant  section  and 
material  is  directly  proportional  to  the  length  and  inversely 
proportional  to  the  area  of  the  cross-section.”  1 The  neglect 
of  quantitative  determination  of  the  proportionate  variations 
of  the  antecedent  and  consequent  was  a glaring  defect  in  the 
inductive  systems  both  of  Mill  and  of  Bacon. 

Through  the  representation  of  the  various  stages  of  such 
variation,  it  is  also  possible  to  establish  the  upper  and  lower 
limits  beyond  which  the  cause  does  not  produce  the  corre- 
sponding effect;  as  in  Weber’s  law  concerning  the  relation 
of  stimulus  to  sensation,  that  stimulus  must  increase  geo- 
metrically in  order  that  the  sensations  increase  arithmeti- 
cally. There  is  an  upper  and  lower  limit  beyond  which  this 
proportion  does  not  hold. 

The  doctrine  of  conservation  of  energy  creates  the  im- 
pression of  continuous  change  in  causation,  in  which  the 
effect  unfolds  out  of  the  cause.  We  do  not  think  of  phenom- 
ena under  this  aspect  as  discrete  events.  More  than  ever, 
in  the  light  of  modern  science,  does  the  old  saying  obtain, 
“ Natura  non  facit  saitum.”  We  no  longer  look  for  catas- 
trophic results  in  nature,  but  regard  causation  as  a con- 
tinuous transfer  of  potential  energy  into  kinetic  or  actual 
energy. 

We  come  now  to  the  consideration  of  the  method  by 
which  the  causal  analysis  is  mediated.  This  is  effected 
through  observation  and  experiment.  Observation  is  some- 
thing more  than  mere  looking  at  phenomena : it  means  con- 
1 Jenkin,  Electricity  and  Magnetism,  p.  83. 


CAUSAL  ANALYSIS  AND  DETERMINATION  213 


centration  of  attention  for  the  purpose  of  research ; it  means 
discriminating  insight,  an  appreciation  of  likeness  and 
difference ; it  means  a penetration  beneath  surface  appear- 
ances, and  an  apprehension  of  the  essential  features  of  the 
objects  of  perception.  Experiment  consists  in  modifying 
the  elements  which  form  the  complex  antecedent  in  order  to 
observe  the  resultant  effect  upon  the  corresponding  conse- 
quent. Forces  may  be  added  or  subtracted ; their  intensity 
may  be  varied,  increased,  or  decreased ; the  circumstances 
or  conditions  may  be  altered.  Herschel  speaks  of  observa- 
tion and  experiment,  as  passive  and  active  observation 
respectively.  When  we  interfere  to  change  the  course  of 
nature,  or  to  bring  natural  forces  within  the  range  of  our 
observation,  we  are  experimenting.  Observation  is  prelimi- 
nary to  experiment,  and  suggests  the  lines  along  which 
experiment  should  proceed.  An  observation  that  sees  the 
parts  in  the  whole  and  the  whole  in  the  parts,  is  in  itself 
an  analysis  of  a phenomenon,  in  course  of  which  process 
causal  relations  must  be  disclosed.  The  scientific  spirit 
demands  absolute  veracity  in  observation.  One  ought  not 
to  be  blind  to  facts  even  though  they  tend  to  contradict 
preconceived  theories.  Bacon  has  observed  that  “ men  mark 
when  they  hit,  never  mark  when  they  miss.”  We  must 
strive  against  a natural  tendency  to  see  things  as  we  would 
have  them,  and  not  as  they  strictly  are. 

We  must  also  carefully  distinguish  between  observed 
facts,  and  inferences  which  we  instinctively  draw  from 
these  facts.  Observation  is  preliminary  to  an  inductive 
inference,  therefore  it  must  not  itself  involve  an  inference, 
or  we  should  be  arguing  in  a circle.  An  interesting  illus- 
tration of  the  difference  between  observation  and  inference 
based  upon  it,  is  narrated  in  the  life  of  Faraday:  “An 
artist  was  once  maintaining  that  in  natural  appearances  and 
in  pictures,  up  and  down,  and  high  and  low,  were  fixed  in- 
dubitable realities;  but  Faraday  told  him  that  they  were 
merely  conventional  acceptations,  based  on  standards  often 


214 


INDUCTIVE  LOGIC 


arbitrary.  The  disputant  could  not  be  convinced  that  ideas 
which  he  had  hitherto  never  doubted,  had  such  shifting 
foundations.  ‘ Well,’  said  Faraday,  ‘ hold  a walking-stick 
between  your  chin  and  great  toe;  look  along  it  and  say 
which  is  the  upper  end.’  The  experiment  was  tried,  and 
the  artist  found  his  idea  of  perspective  at  complete  variance 
with  his  sense  of  reality;  either  end  of  the  stick  might  be 
called  upper,  — pictorially  it  was  one,  physically  it  was  the 
other.” 1 

This  indicates  how  readily  our  inferences  and  observations 
blend,  and  how  difficult  it  is  to  separate  them  in  conscious- 
ness. De  Morgan  has  pointed  out  that  there  are  four  ways 
of  one  event  seeming  to  follow  another,  or  to  be  connected 
with  it,  without  really  being  so  : — 

(1)  Instead  of  A causing  B,  our  perception  of  A may 
cause  B.  A man  dies  on  a certain  day  which  he  has  always 
regarded  as  his  last  through  his  own  fears  concerning  it. 

(2)  The  event  A may  make  our  perception  of  B follow, 
which  otherwise  would  happen  without  being  perceived. 
It  was  thought  that  more  comets  appeared  in  hot  than  cold 
summers ; no  account,  however,  was  taken  of  the  fact  that 
hot  summers  would  be  comparatively  cloudless,  and  afford 
better  opportunities  for  the  discovery  of  comets. 

(3)  Our  perception  of  A may  make  our  perception  of  B 
follow.  This  is  illustrated  by  the  fallacy  of  the  moon’s 
influence  in  the  dissipation  of  the  clouds.  When  the  sky  is 
densely  clouded,  the  moon  would  not  be  visible  at  all;  it 
would  be  necessary  for  us  to  see  the  full  moon  in  order  that 
our  attention  should  be  strongly  drawn  to  the  fact,  and  this 
would  happen  most  often  on  those  nights  when  the  sky  is 
cloudless. 

(4)  B is  really  the  antecedent  event,  but  our  perception 
of  A,  which  is  a consequence  of  B,  may  be  necessary  to 
bring  about  our  perception  of  B.  Upward  and  downward 
currents  are  continually  circulating  in  the  lowest  stratum  of 

1 Gladstone,  Michael  Faraday,  pp.  165,  166. 


CAUSAL  ANALYSIS  AND  DETERMINATION  215 


the  atmosphere ; but  there  is  no  evidence  of  this,  until  we 
perceive  cumulous  clouds,  which  are  the  consequence  of  such 
currents.1 

There  are  certain  natural  limitations  to  observation,  as 
things  too  minute  to  be  seen,  too  swift  to  be  carefully  exam- 
ined; there  are  sounds  which  some  ears  can  detect,  while 
others  cannot,  and  shades  that  some  eyes  cannot  discriminate. 
There  are  effects  proceeding  from  certain  causes  that  are  so 
slight  that  we  fail  to  observe  them,  and  yet  erroneously  infer 
that  they  do  not  exist.  Professor  Tyndall  has  given  a strik- 
ing illustration  of  the  difference  of  auditory  power  in  two 
individuals  ; he  says  : “ In  crossing  the  Wengern  Alp  in  com- 
pany with  a friend,  the  grass  at  each  side  of  the  path  swarmed 
with  insects  which  to  me  rent  the  air  with  their  shrill  chirrup- 
ing. My  friend  heard  nothing  of  this,  the  insect  music  lying 
quite  beyond  his  limit  of  audition.”  2 Much  has  been  done 
by  inventive  skill  to  increase  our  powers  of  observation,  and 
at  the  same  time  to  render  them  more  accurate,  as  the  tele- 
scope, microscope,  the  vernier  for  precise  measurement  of 
minute  differences  of  magnitude,  the  chronograph  for  time 
measurements,  self-registering  thermometers,  the  thermopile, 
galvanometers,  etc.  One  of  the  chief  problems  of  scientific 
method  is  to  overcome  natural  limitations  of  observation 
through  mechanical  devices. 

Observations  on  a large  scale  and  over  a considerable 
period  of  time  must  sometimes  be  taken  in  order  to  disclose 
tendencies  as  seen  only  in  the  average  or  the  mean  of  the 
observed  results.  Thus  meteorological,  vital  statistics,  and 
others  of  a like  kind,  must  extend  over  a large  area,  and 
embrace  a large  number  of  instances  in  order  to  reach 
results  of  any  value.  It  is  known  that  Tycho  Brahe  made 
an  immense  number  of  most  exact  records  of  the  positions  of 
the  heavenly  bodies  with  the  aid  of  the  best  of  astronomical 

1 Quoted  by  Jevons,  Principles  of  Science,  pp.  409-411. 

2 Tyndall,  On  Sound,  pp.  73,  74. 


216 


INDUCTIVE  LOGIC 


instruments,  and  these  records  afterwards  became  the  foun- 
dation of  Kepler’s  laws  and  of  modern  astronomy.1 

The  faculty  for  accurate  observation  can  be  increased  by 
acquiring  the  habit  of  examining  carefully  everything  within 
the  field  of  vision.  We  fail  to  see  many  things  because  we 
.fall  into  the  easy  way  of  passing  them  by  without  noting 
their  presence  or  appreciating  their  significance.  It  was 
said  of  Charles  Darwin  by  his  son  that  “ he  wished  to  learn 
as  much  as  possible  from  every  experiment,  so  that  he  did  not 
confine  himself  to  observing  the  single  point  to  which  the 
experiment  was  directed,  and  his  power  of  seeing  a number 
of  other  things  was  wonderful.”  2 The  open-eyed  vision  is 
the  prime  requisite  for  scientific  investigation. 

The  limitations  of  observation  naturally  lead  to  experi- 
ment, whose  special  function  is  to  so  modify  phenomena  as 
to  bring  a suspected  causal  element  more  prominently  into 
notice.  This  can  be  done  by  intensifying  the  force  in  ques- 
tion, or  by  neutralizing  all  other  elements  in  combination 
with  it,  so  that  the  sole  effect  of  this  force  in  actual  opera- 
tion can  be  observed.  When  the  cause  is  not  a simple  ele- 
ment, but  a combination,  then  the  problem  is  to  vary  the 
conditions  so  that  but  one  possible  combination  can  be  opera- 
tive alone,  and  note  the  corresponding  effect.  Given  a 
certain  number  of  elements,  the  number  of  possible  com- 
binations is  mathematically  determinate,  and  can  be  tried 
seriatim  until  all  possibilities  are  exhausted.  Venn  has 
given  a long  and  interesting  illustration  of  this  in  his  Em- 
pirical Logic.3  All  combinations  need  not  be  tried,  how- 
ever ; for  many  will  be  seen  to  be  either  impossible  or 
irrelevant.  The  aim  is  to  obtain  an  antecedent  which  shall 
consist  either  of  a simple  element,  or  a combination  such 
that  with  its  presence  the  effect  in  question  is  present  also, 
but  with  its  disappearance  the  effect  is  wanting. 

1 Gore,  The  Art  of  Scientific  Discovery,  p.  316. 

2 Life  and  Letters  of  Charles  Daruiin,  Vol.  I.  p.  122. 

8 pp.  402  ff. 


CAUSAL  ANALYSIS  AND  DETERMINATION  217 


It  is  not  sufficient  to  note  merely  the  presence  of  an  ante- 
cedent connected  with  a corresponding  consequent;  scien- 
tific determination  consists  also  in  proving  the  absence  of 
the  suspected  cause  in  cases  where  the  given  effect  is  not 
present.  This  is  called  determination  by  negation.  A 
proposition  which  is  held  affirmatively  has  only  a vague 
significance;  it  must  be  determined  within  definite  limits 
assigned  to  it  by  virtue  of  what  it  is  not.  Defining  means 
to  set  limits  to  a term ; these  limits  grow  out  of  the  nature 
of  the  thing  itself.  The  negative  judgment  marks  a transi- 
tion always  from  that  which  is  indefinite  and  incoherent 
to  that  which  is  definite  and  coherent.1 

This  may  be  illustrated  in  the  concrete,  when  in  dissec- 
tion one  is  tracing  a nerve;  it  is  followed  throughout  its 
course  by  a series  of  negative  judgments  though  they  be 
unexpressed : This  is  not  a nerve,  but  an  artery ; this  is  not 
a nerve,  but  a vein ; this  is  not  a nerve,  but  a filament,  or 
shred  of  muscle,  etc.  So  we  rise  through  negative  discrim- 
ination to  a clear  apprehension  of  an  object  under  investi- 
gation. The  original  proposition  must  be  readjusted  with 
every  new  negative  determination.  It  sometimes  happens 
that  the  original  proposition  is  completely  negatived  by  the 
negative  determination,  sometimes  again  it  is  confirmed. 

A proposition  that  has  not  been  worked  over  through  such 
a process  has  no  real  logical  worth  or  scientific  value.  There- 
fore in  the  analysis  of  phenomena  when  the  suspected  cause 
and  effect  are  combined  in  a proposition,  it  can  at  first  be 
held  only  tentatively.  It  must  be  confirmed  negatively,  or 
else  readjusted  to  conform  to  the  negative  requirements. 
Suppose  we  have  given  that  A is  followed  by  B as  far  as  we 
have  been  able  to  observe.  We  may  proceed  by  experiment, 
to  multiply  instances  of  A’s  connection  with  B,  but  still  the 
causal  relation  is  not  absolutely  proved.  We  must  go  on 
to  show  that  in  all  cases  of  not- A there  is  not-jB,  or  in  all 
cases  of  not-U  there  is  not- A.  Negative  experiment  pro- 

1 See  p.  74. 


218 


INDUCTIVE  LOGIC 


duces  the  contrapositive,  or  the  converse  contrapositive,  of 
the  proposition  under  investigation,  which  deductively  neces- 
sitates the  validity  of  the  original  proposition. 

This  is  substantially  Mill’s  method  of  difference,  that  if 
an  instance  in  which  the  phenomenon  under  investigation 
occurs,  and  an  instance  in  which  it  does  not  occur,  have 
every  circumstance  save  one  in  common,  and  that  one  oc- 
curring only  in  the  former,  the  circumstance  in  which  alone 
the  two  instances  differ  is  the  effect  or  cause  or  a necessary 
part  of  the  cause  of  the  phenomenon.  This  method  will 
be  described  later;  it  is  the  main  inductive  method,  the 
others  being  largely  modifications  of  it.  A negative  in- 
stance which  is  established  concerning  relations  of  not-M 
and  not-B  is  absolutely  conclusive,  inasmuch  as  not- A is 
the  contradictory  of  A,  and  uot-B  is  the  contradictory  of  B. 
They  are  mutually  exclusive.  No  other  possibility  can  be 
forthcoming,  and  the  experimental  analysis  is  exhaustive. 
Professor  Tyndall  gives  the  following  account  of  an  experi- 
ment to  determine  the  cause  of  resonance.  “ I hold  a vibrat- 
ing tuning-fork  over  a glass  jar  eighteen  inches  deep ; but 
you  fail  to  hear  the  sound  of  the  fork.  Preserving  the  fork 
in  its  position,  I pour  water  with  the  least  possible  noise 
into  the  jar.  The  column  of  air  underneath  the  fork  be- 
comes shorter  as  the  water  rises.  The  sound  augments  in 
intensity,  and  when  the  water  reaches  a certain  level,  it 
bursts  forth  with  extraordinary  power.  I continue  to  pour 
in  water,  the  sound  sinks,  and  becomes  finally  as  inaudible 
as  at  first.” 1 

From  this  it  is  inferred  that  a certain  column  of  water  of 
definite  height  is  necessary  to  the  production  of  the  sound, 
for  above  and  below  the  limits  no  sound  is  heard.  This 
experiment  also  indicates  that  which  is  most  important  in 
causal  determination,  — a variation  in  cause  accompanied  by 
a variation  in  effect,  as  also  a maximum  and  minimum  as 
regards  the  intensity  of  the  sound.  Experiment  proceeds 
1 Tyndall,  On  Sound,  p.  172. 


CAUSAL  ANALYSIS  AND  DETERMINATION  219 


upon  the  supposition  of  the  measurableness  of  phenomena, 
and  seeks  numerically  expressible  results  in  this  regard. 
For  instance,  by  different  experiments,  Tyndall  proved  that 
the  length  of  the  column  of  air  which  resounds  to  the  fork 
in  a maximum  degree  of  intensity  is  equal  to  one-fourth  of 
the  length  of  the  wave  produced  by  the  fork.1 

The  negative  determination  of  a suspected  connection 
of  cause  and  effect  must  be  precise  in  order  to  establish 
the  causal  relation  with  that  degree  of  accuracy  which  is 
demanded  in  a truly  logical  and  scientific  method.  Upon 
this  point,  Bosanquet  has  a very  suggestive  passage  : “ The 
essence  of  significant  negation  consists  in  correcting  and 
confirming  our  judgment  of  the  nature  of  a positive  phe- 
nomenon by  showing  that  just  when  its  condition  ceases, 
just  then  something  else  begins.  The  ‘Just-not’  is  the  im- 
portant point,  and  this  is  only  given  by  a positive  negation 
within  a definite  system.  You  want  to  explain  or  define  the 
case  in  which  A becomes  B.  You  want  observation  of  not-B, 
but  almost  the  whole  world  is  formally  or  barely  not-B, 
so  that  you  are  lost  in  chaos.  What  you  must  do  is  to  find 
the  point  within  A where  Ax  which  is  B,  passes  into  A2 
which  is  C,  and  that  will  give  you  the  just-not-B  which  is 
the  valuable  negative  instance.” 2 For  example,  in  Professor 
Tyndall’s  experiment,  the  significant  negative  instance  was 
this,  — when  the  water  in  the  tube  reached  just  that  height 
when  for  the  first  time  during  the  experiment  no  sound  was 
audible.  The  discriminating  observation  that  can  mark  and 
measure  the  precise  point  of  transition  from  sound  to  no 
sound,  has  determined  accurately  the  conditions  necessary 
to  produce  the  sound,  and  precisely  define  their  limita- 
tions. 

In  all  observation  and  experiment,  the  following  possi- 
bilities should  be  kept  before  the  mind  in  order  to  avoid  a 
hasty  conclusion  in  reference  to  a seeming  causal  connec- 

1 Tyndall,  On  Sound,  p.  174. 

2 Bosanquet,  The  Essentials  of  Logic,  p.  134. 


220 


INDUCTIVE  LOGIC 


tion.  We  may  think  that  we  have  discovered  the  relation 
that  if  there  is  A,  then  there  must  be  B,  and  the  one  there- 
fore the  cause  of  the  other,  but  it  may  happen  that 

1.  Both  A and  B are  effects  of  another  cause  and  are 
thereby  related  coordinately  in  reference  to  it. 

2.  A may  be  merely  a liberating  circumstance,  or  an  inva- 
riable accompaniment  of  B. 

3.  A may  not  be  the  cause  of  B,  but  only  an  element  of  a 
complex  collocation  which  is  the  cause  of  B. 

4.  Each  separate  instance  of  B may  so  differ  as  to 
respond  to  the  action  of  A in  a manner  different  from  the 
others. 

5.  A may  be  related  to  B in  a system  of  such  a nature 
that  the  system  in  continuously  developing  new  effects 
causes  B,  as  the  introduction  of  medicine  into  an  organism 
whose  forces  are  themselves  effecting  a healing  process. 

6.  It  is  often  very  difficult  to  tell  whether  A is  the  cause 
of  B,  or  B the  cause  of  A,  as  in  districts  where  drunkenness 
and  poverty  are  prevalent,  or  cases  of  moral  and  intellectual 
feebleness.  Which  is  the  cause  ? and  which  the  effect  ? In 
many  cases  such  as  these,  the  forces  react  upon  each  other, 
the  effect  tending  to  increase  the  intensity  of  the  cause. 

7.  The  connection  of  A and  B may  be  one  of  mere  coin- 
cidence, and  not  of  a causal  nature  whatsoever.  Newton 
was  much  impressed  with  the  apparent  connection  between 
the  seven  intervals  of  the  octave,  and  the  fact  that  the 
colors  of  the  spectrum  divide  into  a like  series  of  seven 
intervals.  And  yet  there  is  no  causal  connection  that  can 
be  proved  to  exist  between  the  two. 

The  more  we  dwell  upon  these  various  possibilities,  ths 
more  are  we  impressed  with  the  extreme  complexity  in 
which  the  relation  of  cause  and  effect  is  involved.  The 
investigator  must  bring  to  his  research  the  spirit  of  patience 
and  perseverance,  as  well  as  a clear  vision  and  discriminat- 
ing insight.  Sir  John  Lubbock,  in  his  observations  upon 
the  habits  of  ants,  says  that  at  one  time  he  watched  an  ant 


CAUSAL  ANALYSIS  AND  DETERMINATION  221 


from  six  in  the  morning  until  a quarter  to  ten  at  night,  as 
she  worked  without  intermission  during  all  that  time.1  It 
is  to  such  patient  investigators  that  nature  reveals  her 
secrets. 

1 Sir  John  Lubbock,  Scientific  Lectures,  p.  73. 


CHAPTER  VI 


MILL’S  INDUCTIVE  METHODS— THE  METHOD  OF 
AGREEMENT 

There  are  certain  specific  methods  by  which  a supposed 
relation  of  cause  and  effect  may  be  tested.  Before  applying 
any  method  however  to  concrete  instances,  there  is  naturally 
in  mind  some  suspected  causal  relation  which  is  the  result 
of  one  or  both  of  the  two  preliminary  inductive  processes. 

As  we  have  seen,  these  primary  processes  in  inductive  in- 
quiry are  induction  by  simple  enumeration,  and  induction 
by  analogy.  By  the  enumeration  of  the  special  cases  in 
which  we  have  found  a significant  coexistence  or  sequence, 
a causal  relation  is  suggested  as  a possible  or  probable  ex- 
planation. By  analogy  also  a causal  relation  is  suggested 
on  the  basis  that  a given  phenomenon  which  in  essential 
particulars  resembles  another  phenomenon  whose  cause  or 
effect  is  already  known  will,  in  all  probability,  have  a like 
cause  or  effect.  Enumeration  and  analogy  thus  suggest  a 
probable  explanation  which  is  not  as  yet  proved,  but  which 
ranks  as  a tentative  hypothesis.  The  natural  history,  there- 
fore, of  the  final  product  of  the  inductive  process  recognizes 
the  initial  stages  of  enumeration  and  analogy  leading  to 
some  preliminary  hypothesis,  which  is  to  be  tested  by  one 
or  more  of  the  specific  methods  of  scientific  investigation. 
These  methods  have  been  formulated  by  John  Stuart  Mill 
and  are  especially  associated  with  his  name.  They  are  as 
follows : — 

1.  The  Method  of  Agreement.  2. 

2.  The  Method  of  Difference.  X.3  g 

3.  The  Joint  Method  of  Agreement  and  Difference.  3 

222 


MILL’S  INDUCTIVE  METHODS 


223 


4.  The  Method  of  Concomitant  Variations.  2.5  S 

5.  The  Method  of  Residues.  2 ir*J  f 

The  method  of  agreement  consists  in  inferring  the  exist- 
ence of  a causal  relation,  when  in  a number  of  varying 
instances  it  is  observed  that  the  supposed  cause  is  always 
accompanied  by  the  phenomenon  in  question,  as  correspond- 
ing effect. 

The  method  of  difference  is  the  comparing  of  an  instance 
where  the  supposed  cause  is  present,  accompanied  by  the 
corresponding  effect,  with  an  instance  having  precisely  the 
same  setting,  but  where  the  supposed  cause  is  withdrawn, 
the  effect  also  disappearing  ; the  inference  of  a causal  rela- 
tion is  then  permissible. 

The  joint  method  of  agreement  and  difference  is  the  com- 
paring of  instances  where  the  supposed  cause  is  present, 
with  similar  instances  where  it  is  absent ; if  the  correspond- 
ing effect  is  present  in  the  former,  and  absent  in  the  latter, 
group  of  instances,  a causal  relation  may  be  inferred.  This 
differs  from  the  method  of  difference,  that  in  the  latter  the 
same  instance,  now  with,  and  again  without,  the  presence  of 
the  suspected  cause,  is  the  subject  of  observation ; in  the 
joint  method  it  is  a number  of  instances  with,  compared 
with  a number  of  similar  instances  without,  the  presence  of 
the  supposed  cause. 

The  method  of  concomitant  variations  consists  in  so  modi- 
fying any  given  phenomenon  that  the  supposed  cause  will 
vary  in  intensity;  then  a corresponding  variation  in  the 
accompanying  effect  is  evidence  of  a causal  relation. 

The  method  of  residues  consists  in  the  analysis  of  a given 
complex  phenomenon,  in  which  all  elements  save  one  of  the 
antecedent  are  known  to  be  related  severally  in  a causal 
manner  to  all  elements  save  one  of  the  consequent;  then 
the  residual  element  of  the  one  may  be  regarded  as  the 
cause  of  the  residual  element  of  the  other. 

These  methods,  it  is  true,  deal  only  with,  concrete 


224 


INDUCTIVE  LOGIC 


instances ; but,  in  so  far  as  these  instances  discover  an 
underlying  causal  connection,  they  thereby  furnish  sufficient 
ground  for  a complete  generalization,  and  warrant  the  induc- 
tive procedure  from  special  cases  to  the  universal. 

We  will  now  examine  these  methods  more  in  detail.  The 
brief  outline  above  is  intended  merely  to  give  a general  idea 
of  the  methods,  that  it  may  lead  to  a better  understanding  of 
the  more  exact  statement  of  their  nature  and  characteristics. 

The  Method  of  Agreement.  — The  more  precise  statement 
of  this  method  is  given  in  the  first  canon  of  Mill,  which  is 
substantially  as  follows:  — 

If  two  or  more  instances  of  the  phenomenon  under  investi- 
gation have  only  one  circumstance  in  common,  the  circum- 
stance in  which  alone  all  the  instances  agree  is  the  probable 
cause  (or  effect)  of  the  given  phenomenon,  or  sustains  some 
causal  relation  to  it. 

The  above  is  based  upon  the  causal  axiom  that  the  constant 
elements  which  emerge  in  any  given  series  of  similar  phe- 
nomena are  to  be  considered  as  connected  in  some  manner 
with  the  cause  of  the  phenomena;  but  that  the  variable 
elements  are  not  connected  with  the  phenomena  in  any 
causal  manner  whatsoever. 

The  method  of  agreement  is  illustrated  in  the  investiga- 
tion of  the  very  common  phenomenon  of  the  transformation 
of  substances  from  the  solid  to  the  liquid  state.  What  is 
the  one  circumstance  which  is  always  present  when  we  con- 
sider the  melting  of  such  widely  different  substances  as 
butter,  ice,  lead,  iron,  etc.  ? In  all  instances,  to  whatsoever 
extent  they  may  be  multiplied,  of  the  change  from  solid  to 
liquid  states,  heat  has  been  observed  to  be  present,  and 
is  thereby  indicated  as  the  likely  cause  of  the  phenomenon 
in  question.  The  method  may  be  represented  through  the 
use  of  symbols  which,  according  to  Mill,  are  capital  letters 
to  denote  antecedents,  and  smaller  letters  to  denote  corre- 
sponding consequents.  Let  the  following  be  a number 
of  different  instances  with  the  antecedents  and  con- 


THE  METHOD  OF  AGREEMENT 


225 


sequents  arranged  in  order,  and  represented  as  above  in- 
dicated : — 

ABC abc. 

ADE ade. 

AMN amn. 

etc.  etc. 

By  inspection  of  such  a table  of  instances  thus  analyzed, 
and  symbolically  represented,  it  will  be  readily  seen  that  A 
is  the  only  element  common  to  all  the  antecedents,  while 
a is  the  only  one  common  to  all  the  consequents.  The  in- 
ference, therefore,  is  that  A is  the  cause  of  a.  It  has  been 
objected  to  this  system  of  representation  that  it  artificially 
arranges  the  elements  of  antecedent  and  consequent,  as 
though  there  were  a number  of  distinct  cause-elements,  each 
connected  with  a correspondingly  distinct  effect-element,  and 
it  produces  the  impression  that  it  is  quite  an  easy  matter 
to  see  how  these  causal  pairs  are  thus  separately  related.1 
As  nature  presents  her  phenomena  to  us,  however,  there  is 
such  complexity  throughout,  that  the  analysis  cannot  readily 
distribute  part  to  part  in  appropriate  causal  relations.  To 
avoid  such  an  error  in  notation,  I have  adopted  the  follow- 
ing symbols,  which  will  be  used  hereafter  to  describe  the 
various  methods.  Let  us  take  C as  the  letter  to  represent 
the  supposed  causal  element,  and  S,  the  entire  setting  of 
accompanying  circumstances;  let  e denote  the  corresponding 
effect,  and  s the  sum  total  of  the  attendant  consequences. 
The  causal  relation  will  be  then  indicated,  according  to  the 
method  of  agreement,  as  follows : — 

S + C s+e. 

S'  + C s'  + e. 

S"  + C s"  + e. 

Here  the  setting  changes  throughout,  as  indicated  by  S, 
S',  S",  etc.,  but  C remains  constant  in  the  antecedents ; also 
1 Venn,  Empirical  Logic,  p.  411. 


226 


INDUCTIVE  LOGIC 


the  corresponding  setting  in  the  consequents  changes,  as  in- 
dicated by  s,  s',  s",  etc.,  but  e remains  constant  throughout. 
Such  a notation  does  not  attempt  to  represent  just  which 
parts  of  S cause  corresponding  parts  of  s,  nor  by  what  ele- 
ments precisely  S differs  from  S'  and  S",  etc.  It  does  rep- 
resent, however,  the  difference  between  the  variable  and 
constant  elements  of  the  table  of  instances  which  are  ar- 
ranged for  comparison,  and  this  is  the  key  to  disclose  the 
causal  relation. 

As  an  example  of  this  method,  let  us  take  the  physical 
law  that  different  bodies  tend  at  the  same  time  to  absorb 
and  to  emit  the  same  waves  of  light.  It  is  known  that  every 
substance  in  burning  gives  its  own  lines  in  the  spectrum 
analysis,  sodium,  for  instance,  producing  a very  bright  line 
in  the  yellow  portion  of  the  spectrum  in  a definite  locality 
(Line  D,  of  Fraunhofer).  If  now,  instead  of  burning  sodium, 
we  interpose  the  vapor  of  sodium  in  the  path  of  the  ray 
which  should  give  a continuous  spectrum,  the  phenomenon 
is  completely  reversed ; at  the  exact  point  where  there  was 
a bright  line  in  the  spectrum,  a dark  line  now  appears. 
Thus  the  vapor  of  sodium,  acting  as  a screen,  absorbs  the 
rays  which  it  emits  when  it  acts  as  the  luminous  source. 
A similar  effect  is  observed  in  the  case  of  vapors  of  iodine, 
of  strontium,  of  iron,  etc. ; it  may  therefore  be  regarded  as  a 
phenomenon,  admitting  of  generalization  by  induction.1  This 
is  according  to  the  method  of  agreement;  and  we  may  make 
the  following  representation  : — 


Vapor  of  sodium  acting  as  a screen  — S + C 
Vapor  of  iodine  acting  as  a screen  = S'  + C. 
Vapor  of  iron  acting  as  a screen  = S"  -f  C. 
Vapor  of  strontium  acting  as  a screen  = S'"  + C. 

etc.  etc. 


1 Saigey,  The  Unity  of  Natural  Phenomena,  pp.  94,  95. 


THE  METHOD  OF  AGREEMENT 


227 


The  corresponding  consequents  are  : — 

Reversing  bright  sodium  line  to  dark  = s + e. 


Reversing  bright  iodine  line  to  dark  = s'  -f-  e. 

Reversing  bright  iron  line  to  dark  = s"  + e. 

Reversing  bright  strontium  line  to  dark  = s'"  + e. 

etc.  etc. 

Therefore  we  have  : — 

S + C s + e. 

S'  + C s'  +e. 

S"  +C s"  +e. 

S'"  + C s'"  + e. 

etc.  etc. 


In  this  the  constant  C of  the  antecedents  is  the  vapor  of 
any  substance  acting  as  a screen;  the  constant  e is  the 
reversal  in  each  case  of  the  bright  line  of  the  substance  in 
the  spectrum  to  the  corresponding  dark  line  of  the  same. 
From  this  it  is  inferred  that  the  vapor  of  any  substance  acting 
as  a screen  absorbs  exactly  those  rays  which  it  emits  when 
it  acts  as  the  luminous  source. 

It  is  of  great  importance  that  the  instances  selected  for 
observation  or  experiment  be  as  varied  as  possible,  so  that 
widely  differing  phenomena  may  be  gathered  together. 
Then  if  running  through  them  all  there  is  one  common 
element  observed  among  the  antecedents,  and  one  common 
element  among  the  consequents,  the  greater  the  variation 
among  the  instances  the  more  pronounced  will  be  the  signifi- 
cance of  the  constant  elements.  In  the  illustration  given 
the  substances  which  are  so  different  as  iron,  strontium, 
sodium,  iodine,  etc.,  preclude  the  possibility  of  the  resultant 
phenomenon  described  being  due  to  the  peculiar  properties 
of  any  one  metal,  or  group  of  metals.  So  many  phenomena 
and  so  different  in  kind  are  taken  as  to  eliminate  the 
peculiarities  attached  to  any  one  in  particular.  In  this  re- 
spect the  method  is  one  of  elimination.  By  varying  the 


228 


INDUCTIVE  LOGIC 


instances  the  non-essential  is  eliminated,  and  the  essential, 
which  remains  as  the  element  common  to  all,  is  thereby 
emphasized,  and  differentiated  from  all  attendant  circum- 
stances. 

This  method  also  is  one  of  discrimination,  of  discerning 
the  constant  element  under  the  various  changing  forms 
which  it  can  assume,  and  as  such  it  is  similar  to  the  logical 
process  of  the  formation  of  a concept.  The  concept  is  the 
grasping  of  the  universal  element  which  is  present  through 
the  particular  and  concrete  manifestations  of  the  same. 
Through  them  all  there  is  the  like  common  element  which 
is  the  basis  of  the  concept  itself.  So  out  of  many  particular 
instances  the  mind  grasps  the  elements  which  are  common 
to  all,  and  considers  them  as  related  in  a constant  and 
therefore  causal  manner,  which  has  in  itself  the  character 
of  a universal  concept  and  so  admits  of  being  formulated  in 
the  form  of  a law  universal,  which  is  the  end  of  all  induc- 
tion. 

This  method,  moreover,  is  peculiarly  adapted  to  observa- 
tion, the  collating  of  a number  of  instances,  rather  than  to 
experiment.  Instances  cannot  always  be  manufactured,  and 
so  it  may  be  beyond  the  power  of  experiment  to  reproduce 
them.  They  can,  however,  always  be  the  objects  of  research, 
and  as  such  fall  naturally  into  the  field  of  observation. 

The  question  may  properly  be  asked  at  this  point, 
How  does  this  method  differ  from  that  of  induction  by 
simple  enumeration  ? The  latter  we  have  seen  is  never 
satisfactory  because  the  enumeration  cannot  be  complete, 
and  may  be  contradicted  by  an  enlarged  experience.  This 
method  however  is  superior  in  that  it  provides  for  more 
than  simple  enumeration  of  instances  in  which  the  phenome- 
non in  question  has  occurred  ; there  must  be  a corresponding 
analysis  of  the  instances,  accompanied  by  a discriminating 
insight  to  distinguish  the  essential  from  the  unessential. 
Number  of  instances  increases  the  probability  that  the 
variable  elements  have  been  eliminated,  and  enables  the 


THE  METHOD  OF  AGREEMENT 


229 


mind  to  concentrate  upon  tlie  constant  elements  that  remain 
and  are  thereby  disclosed. 

This  method  primarily  admits  of  application  to  instances 
where  a sequence  is  observable  ■ that  is,  where  antecedent 
can  be  distinguished  from  consequent  by  an  appreciable 
time  element.  It  is  however  possible  to  apply  this  method 
to  the  investigation  of  coexistences,  where  it  may  show  that 
either  the  coexisting  elements  are  related  as  cause  and 
effect,  or  that  in  some  causal  manner  they  are  the  correlated 
effect  of  some  cause  sufficient  to  account  for  them  both. 
Many  instances  may  be  adduced  of  the  prevalence  of 
poverty  and  crime  associated  together.  This  may  indicate 
a causal  relation  between  them,  and  yet  a sequence  cannot 
be  observed  of  sufficient  definiteness  to  indicate  which  is 
the  cause,  and  which  the  effect.  The  problem  is  thus  left 
indeterminate,  with  the  suggestion  of  some  other  cause 
which  may  possibly  account  for  them  both.  All  that  the 
method  of  agreement  can  attain,  is  by  collecting  a number 
of  instances  of  diverse  nature  to  indicate  that  in  some  way 
at  least  poverty  and  crime  are  connected  by  causal  ties.  The 
constant  coexistence  of  attributes  in  one  individual  admits 
of  a similar  treatment  and  similar  results.  The  fact  of  the 
high  coloring  of  male  butterflies  in  a large  number  of 
instances,  in  reference  to  a variety  of  species,  indicates  a 
constant  relation  between  the  fact  of  its  being  a male 
and  the  possession  of  brilliant  coloring.  This  inseparable 
association  indicates  a causal  relation,  which,  however, 
cannot  be  more  precisely  determined  by  this  method.  The 
full  explanation  of  the  phenomenon  requires  some  supple- 
mentary hypothesis  depending  upon  conditions  not  disclosed 
by  this  method,  an  hypothesis  such  that  the  high  coloring  has 
the  special  function  of  attracting  the  female  butterfly  and 
has  been  intensified  and  developed  by  natural  selection. 

The  method  of  agreement  is  open  to  criticism  at  several 
points,  and  yet  it  must  be  at  the  beginning  understood  that 
this  method  does  not  rank  as  a final  method.  We  shall 


230 


INDUCTIVE  LOGIC 


soon  see  that  in  many  cases  it  needs  to  be  supplemented  by 
the  method  of  difference,  in  order  either  to  confirm  or  to 
disprove  its  tentative  results.  The  chief  criticisms  that  have 
been  made  of  this  method  may  be  summed  up  as  follows : — 

1.  The  cause  indicated  by  the  method  of  agreement  is 
not  thereby  proved  to  be  the  sole  cause  of  the  phenomenon 
in  question.  We  may  gather  together  a number  of  varied 
instances  where  an  extensive  failure  of  crops  in  the  summer 
has  caused  hard  times  during  the  winter  following.  And 
yet  there  may  be,  and  as  a fact  there  are,  many  other  causes 
which  engender  periods  of  industrial  depression.  We  may 
say,  therefore,  that  this  method  is  capable  of  establishing, 
tentatively  at  least,  a universal  proposition  of  the  form, 
All  x is  y ; it  does  not,  however,  attempt  to  give  any  indica- 
tion, one  way  or  the  other,  regarding  the  validity  of  the  con- 
verse, All  y is  x.  Knowing  the  limitations  of  a method  does 
not  by  any  means  destroy  its  legitimacy  as  a method ; it  rather 
increases  its  efficiency  within  its  proper  sphere,  by  the  more 
exact  knowledge  as  to  the  precise  extent  of  that  sphere  itself. 

2.  It  is  urged  that  while  it  is  possible  to  recognize  in 
most,  if  not  in  all,  cases,  the  common  element  in  the  several 
effects  of  similar  phenomena,  it  is  not  so  easy  a matter  to 
separate  the  common  element  in  the  corresponding  antece- 
dents by  the  simple  method  of  agreement  alone.  For 
instance,  in  Bacon’s  illustration  of  the  investigation  of  the 
cause  of  heat,  he  cites  such  disparate  phenomena  as  the 
sun’s  rays,  friction,  combustion,  etc.  The  element  of  heat 
is  readily  discernible  through  them  all;  but  what  is  the 
common  element  which  operates  as  cause  in  each  case  ? 
There  is  the  difficulty.  Sigwart  illustrates  this  in  the  case 
of  the  phenomenon  of  death.  The  effect  can  be  easily  de- 
tected as  similar  throughout,  but  in  all  the  antecedents  the 
only  property  common  to  them  all  is  life,  and,  therefore,  we 
are  led  into  the  fallacy  of  attributing  to  life  the  cause  of 
death.1  We  must  therefore  acknowledge  that  some  phe- 

1 Sigwart,  Logic,  Vol.  II,  p.  341. 


THE  METHOD  OF  AGREEMENT 


231 


nomena  may  occur  in  such  a variety  and  such  a number  of 
manifestations  as  to  disguise  the  nature  of  the  cause  under 
the  mask  of  a generality  too  indefinite  to  be  recognized.  In 
all  such  instances,  the  method  of  agreement  must  avail  itself 
of  suggestions  received  from  some  other  source,  as  to  the 
nature  of  the  common  element  in  the  antecedents.  Or,  some 
minor  circumstances  attending  the  effect  may  indicate  more 
precisely  the  nature  of  the  cause,  as,  for  instance,  the  pecul- 
iar symptoms  associated  with  death  by  drowning,  which  dif- 
ferentiate it  from  death  due  to  any  other  cause. 

3.  The  common  element  in  the  antecedents  may  prove  to 
be  an  unessential  accompaniment  of  all  the  instances  exam- 
ined. Its  presence,  therefore,  may  have  nothing  whatso- 
ever to  do  with  the  observed  effects.  A number  of  different 
medicines,  for  example,  may  produce  a certain  effect  alike 
in  all  instances.  The  only  common  element  that  can  be 
detected  in  the  various  medicines  examined  may  be  the 
alcohol  which  is  used  as  the  common  vehicle  of  the  different 
drugs,  and  yet  its  effect  may  be  entirely  inert  as  regards  the 
medicinal  qualities  in  question.  The  common  element  really 
efficient  may  be  overlooked,  and  another  common  element 
-which  is  easily  discernible  may  nevertheless  remain  wholly 
inoperative.  This  difficulty  may  be  overcome  by  a more 
thorough  analysis  of  the  phenomena  observed,  which  may 
be  attained  by  a judicious  variation  of  the  instances,  so  as 
to  reveal,  in  turn,  the  precise  effect  of  the  various  simple 
elements  which  together  constitute  the  complex  whole  of 
the  phenomenon  in  question.  The  defects  of  the  method 
in  this  respect  are,  in  a word,  the  defects  of  induction  by 
simple  enumeration. 

4.  The  cause  may  be  present  in  all  the  antecedents,  and, 
notwithstanding  the  corresponding  effect  not  appear,  and 
this,  not  because  the  two  are  not  related  in  a causal  manner, 
but  because  the  cause  is  neutralized  by  the  associated  ele- 
ments which  appear  in  combination  with  it  in  the  various 
antecedents.  Tor  instance,  diphtheria  germs  are  the  cause 


232 


INDUCTIVE  LOGIC 


of  diphtheria,  and  have  been  found  accompanying  this 
disease  in  all  cases  which  have  been  observed.  And  yet 
their  presence  is  often  noted  when  the  disease  itself  does 
not  develop.  The  tendency  existing  is  counteracted  by  the 
condition  of  the  organism  at  the  time,  so  that  the  dread 
bacilli  are  inoperative  and  therefore  harmless.  As  we  have 
seen  before,  the  presence  of  the  effect  necessitates  the  pres- 
ence of  the  corresponding  cause;  but  by  no  means  is  it 
always  true  that  the  presence  of  the  cause  necessitates  the 
effect.  The  cause  always  produces  the  tendency  at  least, 
which  however  may  be  neutralized. 

5.  This  method  is  often  applied  in  a very  careless  way  to 
the  observations  of  persons  who  do  not  possess  the  power 
of  accurate  discrimination,  and  therefore  observed  coinci- 
dences are  hastily  assumed  to  be  particular  instances  of  an 
universal  law.  Such  procedure  leads  to  superstition  and 
prejudice.  It  not  only  warps  the  judgment,  owing  to  its 
illogical  nature,  but  it  also  affects  indirectly  the  man’s 
moral  view,  as  it  implies  a weakness  in  character  as  well 
as  in  mind.  This  criticism  refers  however  to  the  abuse 
rather  than  the  legitimate  use  of  this  method  under  such 
restrictions  as  have  been  already  indicated. 

The  chief  function  of  this  method  is  that  of  suggestion. 
It  indicates  often  only  the  possibility  of  the  existence  of  a 
causal  relation ; in  other  cases  it  leads  to  an  inference  of 
high  probability.  In  all  cases  however  it  marks  merely  the 
preliminary  steps  of  an  investigation  which  should  be  fol- 
lowed up  by  painstaking  experiment.  As  it  is  the  method 
of  observation  chiefly,  it  is  natural  that  it  should  precede 
experiment ; for  it  is  only  by  reflection  upon  our  observa- 
tions that  we  discover  the  nature  and  relations  of  phenomena, 
which  serve  as  data  for  subsequent  experiment. 

I have  selected  several  illustrations  to  indicate  the  various 
fields  of  research  in  which  this  method  of  agreement  has  led 
to  satisfactory  results. 

The  first  refers  to  the  relation  between  the  occurrence  of 


THE  METHOD  OF  AGREEMENT 


233 


financial  crises  and  the  prevalence  of  over-production.  Guyot, 
in  his  Principles  of  Social  Economy,  gives  the  following  in- 
stances: An  enormous  consumption  of  capital  in  the  United 
States  in  the  seventies,  for  the  construction  of  railroads,  was 
followed  by  unusual  commercial  depression.  Then  the  like 
outlay  in  India  for  railway  construction  by  means  of  loans 
and  taxes  which  absorbed  the  whole  circulating  capital  of 
the  Indian  population  was  followed  by  a devastating  fam- 
ine and  general  commercial  paralysis.  Again  in  Germany 
there  was  an  enormous  consumption  of  capital  in  forts  and 
armaments  and  general  military  equipment,  bringing  on  the 
crisis  of  1876-1879.  England  at  the  same  time  was  unduly 
supplying  circulating  capital  to  the  United  States,  Egypt, 
and  her  colonies,  and  a financial  crisis  was  the  result. 
Through  all  these  varying  instances  and  others  of  a like 
nature  which  might  be  added,  the  constant  relation  of  over- 
consumption in  the  antecedents  to  the  industrial  depression 
evident  in  the  effect  indicates  the  one  to  be  the  cause  of  the 
other,  either  in  whole  or  in  part. 

Again  it  is  narrated  in  Brewster’s  Treatise  on  Optics  that 
he  accidently  took  an  impression  from  a piece  of  mother-of- 
pearl  in  a cement  of  resin  and  beeswax,  and,  finding  the 
colors  repeated  upon  the  surface  of  the  wax,  he  proceeded 
to  take  other  impressions  in  balsam,  fusible  metal,  lead, 
gum  arabic,  isinglass,  etc.,  and  always  found  the  iridescent 
colors  the  same.  His  inference  was  that  the  form  of  the 
surface  is  the  real  cause  of  such  color  effects.1  The  com- 
mon element  which  appears  in  all  the  antecedents  is  evidently 
the  same  form  impressed  upon  each,  which  was  originally 
received  from  the  mother-of-pearl.  The  cause  is  moreover 
independent  of  the  nature  of  the  substance  in  each  case 
which  received  the  impression  upon  its  surface,  because 
such  a variety  of  substances  was  chosen  as  to  eliminate  the 
individual  nature  of  each  as  an  influencing  factor  in  the 
result.  In  this  experiment  we  see  the  advantage  of  varying 
1 Quoted  by  Jevons,  Principles  of  Science,  p.  419. 


234 


INDUCTIVE  LOGIC 


the  instances  as  far  as  possible  for  this  very  purpose  of 
eliminating  all  irrelevant  elements.  Similar  experiments 
have  proved  like  results  in  reference  to  the  colors  exhibited 

thin  plates  and  films.  Here  the  rings  and  lines  of  color 
have  been  found  to  be  nearly  the  same  whatever  may  be 
the  nature  of  the  substance.  A slight  variation  in  color  is 
due  to  the  refractive  index  of  the  intervening  substance. 
With  this  exception,  the  nature  of  the  substance  is  not 
operative  in  producing  the  color  effect,  but  the  form  alone. 

The  celebrated  scientist,  Pasteur,  in  the  year  1868  was 
carrying  on  his  investigations  as  to  the  cause  of  the  blight 
then  devastating  the  silkworms  of  France.  One  of  his  ex- 
periments consisted  in  selecting  thirty  perfectly  healthy 
worms  from  moths  that  were  entirely  free  from  the  cor- 
puscles, which  latter  are  the  germs  of  disease,  or  at  that 
time  suspected  to  be  the  germs  of  disease.  Then,  rubbing 
a small  corpusculous  worm  in  water,  he  smeared  the  mix- 
ture over  the  mulberry  leaves.  Assuring  himself  that  the 
leaves  had  been  eaten,  he  watched  the  consequences  day  by 
day.  One  after  the  other  the  worms  languished ; all  showed 
evidences  of  being  the  prey  of  the  corpusculous  matter,  and 
finally,  within  one  month’s  time,  all  died.  Pasteur’s  infer- 
ence naturally  was  that  the  corpuscles  had  produced  the  death. 
Of  course  his  results  were  not  founded  upon  this  experiment 
alone,  but  other  experiments,  carried  on  in  many  different 
ways,  served  to  corroborate  the  causal  relation  which  the 
experiment  just  described  had  suggested  as  at  least  highly 
probable. 

In  medicine  also  the  method  of  agreement  is  often  used 
with  effect.  Certain  drugs  are  administered  in  a number  of 
cases  and  the  results  noted.  A uniform  effect  consequent 
upon  the  administration  of  a given  drug  indicates  a causal 
connection  capable  of  generalization.  Not  only  are  subjects 
in  disease,  but  also  in  health,  selected,  and  the  effects  upon 
both  the  normal  and  morbid  natures  compared.  Thus  a 
variation  in  instances  is  secured.  If  a number  of  different 


THE  METHOD  OF  AGREEMENT 


235 


drugs  produce  like  effects,  the  question  at  once  suggests 
itself,  What  is  the  property  common  to  them  all  ? The 
method  of  agreement  often  gives  some  indication  of  this, 
■when  the  elimination  of  the  inert  properties  can  be  accom- 
plished through  a sufficient  variation  of  instances.  The 
difficulty  lies,  however,  in  this  very  thing,  to  so  vary  the  in- 
stances as  to  disclose  the  efficient  element  present  in  them  all. 
Various  medicines  present  a complex  nature  of  such  a char- 
acter that  it  is  extremely  difficult  to  discriminate  the  precise 
effects  which  the  several  component  parts  individually 
exercise. 

The  method  of  agreement  is  also  used,  perhaps  uncon- 
sciously, in  the  conduct  of  the  everyday  affairs  of  life. 
Whenever  different  phenomena  in  our  experience  present 
certain  characteristics  of  a constant  nature,  we  are  at  once 
led  to  suspect  a causal  connection,  and  to  start  upon  a more 
searching  investigation  of  the  same.  Too  often  however 
the  supplementary  investigation  is  omitted,  and  the  mind 
rests  content  with  a few  surface  resemblances  that  lead  to 
a hasty  generalization  without  being  more  precisely  and 
adequately  determined. 


CHAPTER  VII 


THE  METHOD  OF  DIFFERENCE 

The  method  of  agreement,  as  we  have  seen,  presents  a 
causal  relation  as  a suggestion,  admitting  of  a high  degree 
of  probability  it  may  be,  but  requiring  to  be  tested  by  some 
more  scientific  method.  This  is  accomplished  by  the  method 
of  difference.  Here  a phenomenon  is  observed,  in  which 
the  supposed  cause-element  and  effect-element  appear ; then 
while  all  other  circumstances  and  conditions  remain  unal- 
tered, the  supposed  cause-element  is  withdrawn,  or  its  force 
adequately  eliminated ; the  immediate  disappearance  of  the 
supposed  effect-element,  consequent  upon  this,  indicates  a 
causal  relation  between  the  two.  Or  the  experiment  may 
be  made  in  a different  manner,  but  to  the  same  end,  that 
is,  a phenomenon  may  be  characterized  by  the  absence  of 
both  cause-element  and  effect-element;  then,  if  the  intro- 
duction of  the  cause-element  does  not  disturb  the  phenomenon 
in  question,  except  immediately  to  produce  the  effect-ele- 
ment, the  inference  may  be  drawn  that  the  one  is  the 
veritable  cause  of  the  other. 

Canon  of  the  Method  of  Difference.  — If  an  instance  in 
which  the  phenomenon  under  investigation  occurs,  and  an 
instance  in  which  it  does  not  occur,  have  every  circumstance 
save  one  in  common,  that  one  occurring  only  in  the  former; 
the  circumstance  in  which  alone  the  two  instances  differ  is 
the  effect,  or  it  may  be  the  cause,  or  a necessary  part  of  the 
cause,  of  the  phenomenon. 

This  method  admits  of  manifold  illustration  in  our  every- 
day inferences.  A person  is  asleep  in  the  room  with  us, 
and  we  hear  the  loud  noise  of  a slamming  door,  and  observe 

236 


THE  METHOD  OE  DIFFERENCE 


237 


the  person  at  once  awakening  with  a start  and  exclamation. 
We  have  no  hesitancy  in  ascribing  the  awakening  to  the 
noise  immediately  preceding  it.  We  observe  again  some 
one  receiving  a letter  or  telegram,  and  immediately  upon 
opening  it  the  face  grows  white  with  anxiety  and  fear,  the 
hands  tremble,  and  there  are  shown  general  symptoms  of 
perturbation.  The  message  received,  we  say,  has  caused 
the  mental  shock  and  physical  accompaniments. 

Or,  taking  a simple  experiment  in  quite  another  sphere, 
it  was  observed  by  Boyle,  in  1670,  that  an  extract  of  litmus 
was  immediately  turned  red  by  the  introduction  of  an  acid. 
This  subsequently  became  a test  for  the  presence  of  acids, 
the  inference  being  that  an  acid  has  this  capacity  of  chang- 
ing the  litmus  to  a red  color  from  its  original  blue. 

Professor  Tyndall  describes  an  experiment  to  prove  that 
waves  of  ether  issuing  from  a strong  source,  such  as  the  sun 
or  electric  light,  are  competent  to  shake  asunder  the  atoms 
of  gaseous  molecules,  such  as  those  of  the  sulphur  and  oxy- 
gen which  constitute  the  molecule  of  sulphurous  acid.  He 
enclosed  the  substance  in  a vessel,  placing  it  in  a dark  room, 
and  sending  through  it  a powerful  beam  of  light.  At  first 
nothing  was  seen ; the  vessel  containing  the  gas  seemed  as 
empty  as  a vacuum.  Soon,  along  the  track  of  the  beam,  a 
beautiful  sky-blue  color  was  observed,  due  to  the  liberated 
particles  of  sulphur.  For  a time  the  blue  grew  more  intense  ; 
it  then  became  whitish ; and  from  a whitish-blue  it  passed 
to  a more  or  less  perfect  white.  Continuing  the  action,  the 
tube  became  filled  with  a dense  cloud  of  sulphur  particles 
which,  by  the  application  of  proper  means,  could  be  rendered 
visible.1  In  this  series  of  continuous  changes,  we  find  the 
one  antecedent  giving  the  causal  impulse  to  be  the  beam  of 
light.  It  was  the  one  element  introduced  which  started 
the  several  changes  leading  to  the  appearance  of  the  sulphur. 
The  one,  therefore,  is  to  be  regarded  as  the  cause  of  the 
other. 

1 Tyndall,  Use  and  Limit  of  the  Imagination  in  Science,  p.  33. 


238 


INDUCTIVE  LOGIC 


It  is  possible  to  represent  this  method  by  means  of  sym- 
bols in  a manner  similar  to  that  of  the  method  of  agreement. 
Let  C be  the  supposed  cause  and  e the  effect  corresponding, 
while  S and  s denote  the  setting  of  antecedent  and  conse- 
quent respectively.  We  have,  therefore,  the  following  : — 

S + C s - f e. 

Then,  withdrawing  C,  we  have  the  absence  of  e. 

S s. 

The  inference  then  is  that  C is  the  cause  of  e.  Or,  we  may 
have  given 

S s. 

Then  if,  adding  C,  we  find  that  e also  appears,  represented 

by 

S G . . . . . . . . s - f-  e, 

we  infer  that  C and  e have  a causal  connection. 

In  the  method  of  agreement,  a number  of  instances  are 
taken  agreeing  only  in  the  possession  of  two  circumstances, 
— the  cause  and  effect  elements  common  to  them  all.  In 
this  method,  only  two  instances  are  taken,  and  they  must 
be  precisely  alike,  -with  the  one  exception,  — the  presence 
of  two  circumstances  in  one,  that  is,  the  cause  and  the  effect 
elements,  and  the  absence  of  the  same  in  the  other.  In  the 
method  of  agreement,  we  compare  the  various  phenomena 
to  note  wherein  they  agree;  in  the  method  of  difference, 
we  compare  the  two  phenomena  to  note  wherein  they  differ. 
The  logical  axiom  underlying  the  two  methods  is  sub- 
stantially one  and  the  same,  differing  only  in  its  special 
adaptation  in  each  case.  The  former  method  rests  on  the 
assumption,  which  must  be  accepted  as  a fundamental  postu- 
late, that  whatever  can  be  eliminated  from  the  various 
instances  is  not  connected  with  the  phenomenon  under  in- 
vestigation in  any  causal  manner ; and  the  method  of  differ- 


THE  METHOD  OF  DIFFERENCE 


239 


ence  is  based  on  the  postulate  that  whatever  cannot  be  elimi- 
nated is  connected  with  the  phenomenon  by  a causal  law. 

The  method  of  difference  is  evidently  the  method  by 
negation,  which  has  already  been  indicated  as  the  truly 
scientific  process  in  induction.  It  is  also  preeminently  the 
method  of  experiment  rather  than  observation ; for  the  with- 
drawal or  introduction  of  forces  can  only  be  accomplished 
at  will  when  we  bring  the  phenomena  under  experimental 
control.  At  times  nature  herself  may  perform  the  experi- 
ment for  us,  and  we  stand  simply  as  observers  to  note  the 
results.  This  is  especially  the  case  in  the  catastrophic 
phenomena,  such  as  volcanic  eruption,  earthquakes,  etc. 
Generally  speaking,  however,  the  method  of  difference  is  the 
process  of  man’s  manipulation  to  secure  purposed  results  in 
which  a causal  relation  is  disclosed. 

A question  naturally  suggests  itself,  What  is  there  to 
determine  the  precise  mode  of  experiment  ? We  may  have 
given  a concrete  whole  of  extreme  complexity.  In  our  ex- 
periment, which  element  shall  we  proceed  to  eliminate,  in 
order  to  note  the  result  ? An  answer  may  be  given  us 
through  suggestions  received  from  the  results  of  enumera- 
tion, analogy,  or  the  method  of  agreement.  If  it  is  not 
possible  to  avail  one’s  self  of  this  contribution  from  another 
sphere  of  investigation,  then  the  complex  whole  must  be 
broken  up,  as  far  as  possible,  into  its  simplest  component 
parts,  and  one  after  another  these  parts,  singly,  then  in 
pairs,  and  all  other  possible  combinations,  caused  to  be 
withdrawn,  or  their  force  neutralized,  and  the  results  in 
each  case  noted,  as  to  whether  the  effect  under  investigation 
disappears.  The  exhaustion  of  all  possible  combinations 
must  yield  some  definite  result.  Suppose,  for  instance, 
there  is  a complex  antecedent  involving  four  separable  ele- 
ments, as  A,  B,  C,  D.  Withdraw  severally  A,  B,  C,  and  D, 
noting  results ; then  withdraw,  in  turn,  AB,  AC,  AD,  BC, 
BD,  CD,  that  is,  the  possible  combinations  of  four  elements 
taken  two  at  a time  ; then  withdraw  ABC,  then  BCD,  ABD, 


240 


INDUCTIVE  LOGIC 


and  ACD,  that  is,  combinations  of  four  elements  taken  three 
at  a time.1  By  such  a process  there  will  be  disclosed 
whether  one  element  alone  or  whether  a combination  of  two 
or  more  have  produced  the  effect  under  investigation.  The 
practical  difficulty  in  separating  the  elements  of  a complex 
whole,  and  withdrawing  the  several  combinations  from  the 
whole,  renders  this  process  in  many  cases  impossible.  The 
cause,  however,  is  generally  suspected.  It  may  be  suggested, 
as  Ave  have  seen,  by  the  method  of  agreement,  by  analogy, 
or  by  that  insight  which  at  once  declares  certain  combina- 
tions to  be  impossible  and  others  irrelevant.  There  is 
generally  a mental  experiment  in  which  the  judgment 
rejects  unlikely  combinations,  thus  narrowing  the  field  of 
investigation  and  furnishing  a tentative  hypothesis  as  a 
preliminary  to  the  experiments  proper. 

The  method  of  difference  is  open  to  various  criticisms ; 
the  most  important  are  the  following : — 

1.  In  applying  this  method,  we  may  be  easily  misled,  in 
supposing  our  two  instances  are  precisely  alike  Avith  the 
one  exception  of  the  presence  or  absence  of  the  supposed 
cause,  but  in  reality  the  instance  may  differ  radically,  and 
yet  we  may  be  unable  to  detect  this.  A patient  may  have 
medicine  administered  to  him,  and  begin  at  once  rapidly  to 
recover,  and  yet  the  very  taking  of  the  medicine  in  itself 
may  have  made  such  a mental  impression  inducing  confi- 
dence and  hope  that  the  real  cause  of  the  recovery  may  be 
due  wholly  to  this  mental  reaction.  Persons  taking  pills 
composed  of  inert  substances  have  often  given  evidence  of 
bodily  effects  wholly  impossible  to  trace  to  the  medicine 
itself.  And  yet  this  criticism  is  one  of  caution  rather  than 
of  censure;  for  the  defects  are  but  difficulties  which  ex- 
treme care  and  insight  may  overcome. 

2.  It  has  been  objected  that  this  method  may  point  out 
the  cause  in  the  concrete  instance  before  the  experimenter, 

1 This  process  has  been  illustrated  and  criticised  at  length  in  a striking 
manner  by  Venn,  Empirical  Logic,  pp.  101  ff. 


THE  METHOD  OF  DIFFERENCE 


241 


but  that  this  furnishes  no  basis  whatsoever  for  a wider 
generalization  that  the  effect  in  question  is  always  produced 
by  this  cause.  Sigwart  has  illustrated  this  objection  by  the 
instances  in  which  typhus  fever  has  been  traced  to  the 
drinking  of  impure  water.1  The  causal  relation  may  be 
fully  established  in  the  cases  investigated,  but  the  universal 
proposition  does  not  follow  that  wherever  typhus  fever 
appears,  impure  water  has  been  drunk.  This  objection 
applies  especially  to  cases  of  extreme  complexity,  where 
proximate  causes  alone  can  be  discovered,  and  their  ultimate 
nature  which  may  appear  in  various  forms  is  not  revealed ; 
for  instance,  the  impure  water  is  not  in  itself  the  ultimate 
cause  of  the  typhus  fever.  It  contains  the  poison  germs, 
the  real  cause ; they  may  be  introduced  into  the  system  in 
some  other  way.  Care  therefore  should  be  taken  to  reveal 
the  cause  in  and  by  itself,  and  not  the  cause  of  the  cause. 
The  objection,  therefore,  may  be  in  a measure  overcome. 
To  effect  a generalization  of  logical  validity,  it  is  necessary 
to  supplement  the  method  of  difference  by  hypothesis  and 
subsequent  verification,  which  will  be  described  later  on. 

3.  This  method  may  lead  to  error  in  cases  where  the  sup- 
posed causal  element  is  regarded  as  the  cause  in  its  entirety, 
when  it  is  in  reality  but  a part  of  the  cause.  If  one  should 
plant  seed  in  a garden  and  water  only  one-half  of  the  plot, 
and  it  should  follow  that  only  the  watered  part  brought 
forth  the  leaf  and  flower,  then  an  inference  according  to  the 
method  of  difference  might  be  drawn  that  the  water  caused 
the  sprouting  of  the  young  plants.  And  yet  it  must  be  re- 
garded simply  as  contributory  to  the  real  cause.  Such  a 
difficulty  may  be  obviated  by  a careful  discrimination  in  the 
analysis  of  the  phenomenon  investigated. 

4.  Sometimes  a liberating  cause  may  be  revealed  by  a 
strict  interpretation  of  the  method  of  difference,  when  the 
real  cause  is  more  obscure,  and  may  be  overlooked.  A stone 
may  strike  a can  of  dynamite,  and  the  explosion  which 

1 Sigwart,  Logic,  Yol.  II,  p.  120. 


242 


INDUCTIVE  LOGIC 


occurs  may  be  traced  to  the  impact  of  the  stone.  It  is  the 
one  element  of  difference  introduced  in  the  sphere  of  the 
observed  phenomena,  with  the  consequent  result.  The 
force  existing  as  a potential  is  naturally  obscure,  and  apt  to 
elude  observation.  Therefore,  whenever  a cause  disclosed 
by  the  method  of  difference  seems  to  be  out  of  all  propor- 
tion to  the  effect,  it  at  once  suggests  the  probability  that  a 
potential  force  not  discerned  by  our  powers  of  observation 
has  been  the  real  cause,  and  the  former  a conditioning  cause 
merely.  Another  illustration  of  this  is  the  experiment  of 
Priestley,  which  led  to  his  discovery  of  oxygen  in  1774. 
He  placed  some  oxide  of  mercury  upon  the  top  of  quick- 
silver in  an  inverted  glass  tube  filled  with  that  metal  and 
standing  in  mercury ; he  then  heated  the  oxide  by  means  of 
a glass  lens  and  the  sun’s  rays,  and  obtained  a gas,  which 
he  called  “ nitrous  air,”  afterwards  designated  as  oxygen. 
The  heat  in  this  case  was  the  sole  element  of  difference 
between  the  two  instances,  one  in  which  there  was  no  gas, 
and  the  second  after  application  of  the  heat,  when  the  gas 
was  present.  Here  the  heat  must  be  regarded  as  the  liber- 
ating and  not  in  any  sense  the  producing  cause.  Again,  as 
Lotze  says,  “ the  fact  that  with  the  destruction  of  a single 
part  of  the  brain  a definite  psychical  function  ceases,  is  no 
proof  that  just  this  single  part  was  the  organ  which  alone 
produced  that  function.”  1 

In  addition  to  the  difficulties  attending  this  method,  which 
have  been  enumerated  and  which  have  to  do  with  the  logi- 
cal theory  of  the  method,  there  are  also  difficulties  of  a prac- 
tical nature  which  arise  in  the  actual  application  of  this 
method  in  experimental  inquiry.  They  are  as  follows:  — 

1.  Care  must  be  taken  that,  in  the  two  phenomena  com- 
pared, with  and  without  the  supposed  cause,  there  shall  not 
be  an  interval  of  time  elapsing,  in  which  period  some  other 
cause  might  be  introduced  unknown  to  the  investigator,  and 
yet  capable  of  producing  the  result,  or  else  of  neutralizing 
1 Lotze,  Logic,  p.  322. 


THE  METHOD  OF  DIFFERENCE 


243 


some  force  that  is  present  and  itself  capable  of  producing 
the  result.  For  instance,  if  a chemical  compound  be  left 
for  an  appreciable  time,  we  may  notice  certain  changes  and 
be  able  to  assert  positively  that  no  new  element  has  been 
introduced,  and  yet  the  action  of  the  air  may  in  itself  have 
been  sufficient  to  work  these  changes.  When  the  two  phe- 
nomena to  be  compared  can  be  presented  for  inspection 
simultaneously,  this  difficulty  is  obviated.  This  is  illus- 
trated in  an  experiment  devised  to  exhibit  the  presence  of 
light  effects  in  the  spectrum  beyond  the  violet  rays ; that  is, 
beyond  the  place  where  the  spectrum  seems  to  end.  A 
sheet  of  paper  is  taken,  the  lower  part  of  which  is  moistened 
with  a solution  of  sulphate  of  quinine,  while  the  upper  part 
remains  dry.  Let  the  image  of  the  solar  ray  fall  upon  this 
sheet ; the  spectrum  preserves  at  the  top  of  the  sheet  in  the 
dry  portion  of  the  paper  its  ordinary  appearance,  while  in 
the  moistened  portion  a brilliant  phosphorescence  appears 
beyond  the  region  of  the  violet  rays.  Here  the  dry  and  wet 
portions  are  simultaneously  presented,  and  there  is  but  one 
point  of  difference  between  the  two.  The  inference,  there- 
fore, is  readily  drawn  that  the  solution  of  sulphate  of  quinine 
is  a substance  sensitive  to  the  ultra-violet  portion  of  the  sun's 
rays,  the  phosphorescence  being  the  effect  of  these  rays  upon 
the  solution. 

2.  Extreme  care  must  be  taken  that,  in  the  withdrawing 
of  any  element  in  the  course  of  the  experiment,  no  other 
element  is  inadvertently  introduced,  and  that,  in  adding 
any  element,  no  existing  element  or  combination  of  elements 
is  destroyed,  or  their  effect  neutralized.  Mr.  Venn  has  ad- 
mirably illustrated  this  difficulty,  and  I give  the  following 
quotation  in  full  from  him:  “We  suppose  that  when  we 
have  put  a weight  into  one  pan  of  a pair  of  scales  we  have 
done  nothing  more  than  this,  or  can  at  any  rate  by  due  cau- 
tion succeed  in  doing  nothing  more.  But  if  we  exact  the 
utmost  rigidity  of  conditions,  we  easily  see  that  we  have 
done  a great  deal  more.  Our  bodies  are  heavy,  and  there- 


244 


INDUCTIVE  LOGIC 


fore  tlie  mere  approach  to  the  machine  has  altered  the  mag- 
nitude and  direction  of  the  resultant  attraction  upon  the 
scales.  Our  bodies  are  presumably  warmer  than  the  sur- 
rounding air ; accordingly,  we  warm  and  therefore  lighten 
the  air  in  which  the  scales  hang,  and  if  the  two  scales  and 
their  contents  are  not  of  the  same  volume,  we  at  once  alter 
their  weight  as  measured  in  the  air.  Our  breath  produces 
disturbing  currents  of  air.  Our  approach  affects  the  sur- 
face of  the  non-rigid  floor  or  ground  on  which  the  scales 
stand,  and  produces  another  source  of  disturbance,  and  so 
on  through  the  whole  range  of  the  physical  forces.”  1 

In  the  Report  of  the  British  Association,  1881,  an  account 
is  given  of  Professor  G.  H.  Darwin’s  experiments  to  meas- 
ure the  lunar  disturbance  of  gravity  at  the  Cavendish  Lab- 
oratory by  means  of  an  extremely  delicate  pendulum.  It 
was  found  that  approaching  the  pendulum  in  order  to  ob- 
serve its  reading,  the  surface  level  of  the  stone  floor  on 
which  the  instrument  stood  was  deflected  by  the  weight  of 
the  observer.  As  he  stood  to  take  the  reading,  the  shifting 
of  his  weight  from  one  leg  to  the  other  was  perceptible ; so 
it  became  necessary  to  observe  the  reading  by  a telescope 
from  a distance,  or  to  adopt  some  similar  plan.2 

Faraday  was  able  at  will  to  produce  or  remove  a magnetic 
force,  through  the  revealed  properties  of  the  electromagnet. 
Many  of  his  experiments  would  have  been  impossible  if  it 
had  been  necessary  to  remove  a cumbersome  magnet  and 
reinstate  it  again  and  again  in  his  experiments.  The  elec- 
tromagnet however  could  produce  or  destroy  the  presence 
of  magnetic  force  without  any  incidental  perturbations. 
Thus  Faraday  was  enabled  to  prove  the  rotation  of  circu- 
larly polarized  light  by  the  fact  that  certain  light  ceased  to 
be  visible  when  the  electric  current  of  the  magnet  was  cut 
off,  and  instantly  reappeared  when  the  current  was  reestab- 
lished. Faraday  says  of  the  experiment  himself : “ These 

1 Venn,  Empirical  Logic,  p.  416. 

2 Quoted  by  Venn  in  Empirical  Logic , p.  419. 


THE  METHOD  OF  DIFFERENCE 


245 


phenomena  could  be  reversed  at  pleasure,  and  at  any  instant 
of  time,  and  upon  any  occasion,  showing  a perfect  depend- 
ence of  cause  and  effect.”  1 

3.  In  some  cases  it  is  impossible  to  remove  an  element 
which  is  supposed  to  be  the  cause  of  an  effect  under  investi- 
gation. Its  removal  might  cause  the  destruction  or  the  im- 
pairing of  the  whole  phenomenon.  The  force  therefore 
that  cannot  be  eliminated  must  be  neutralized  by  an  equal 
and  opposing  force.  For  instance,  the  force  of  gravity  can- 
not be  eliminated ; it  must  therefore  be  counterbalanced  by 
some  device  of  the  investigator.  In  chemistry  the  removal 
of  an  element  from  a compound  may  be  impossible  without 
destroying  utterly  the  compound  itself ; in  such  a case  also 
a neutralizing  agent  must  be  introduced.  Darwin  wished  to 
prove  that  the  odor  of  flowers  is  attractive  to  insects  irre- 
spective of  the  attraction  of  color.  He  therefore  covered 
certain  flowers  with  a muslin  net,  and  still  the  insects  were 
attracted  to  the  flowers  although  the  color  was  thus  con- 
cealed.2 

The  following  illustrations  may  serve  further  to  exhibit 
the  various  features  of  the  method  of  difference  : — 

Mr.  Robert  Mallet  gives  the  following  interesting  account 
of  his  visit  to  Faraday:  “It  must  be  now  eighteen  years 
ago  when  I paid  him  a visit,  and  brought  some  slips  of 
flexible  and  tough  Muntz’s  yellow  metal,  to  show  him  the 
instantaneous  change  to  complete  brittleness  with  rigidity 
produced  by  dipping  into  pernitrate  of  mercury  solution. 
He  got  the  solution  and  I showed  him  the  facts ; he 
obviously  did  not  doubt  what  he  saw  me  do  before  and 
close  to  him ; but  a sort  of  experimental  instinct  seemed  to 
require  he  should  try  it  himself.  So  he  took  one  of  the 
slips,  bent  it  forward  and  backward,  dipped  it,  and  broke  it 
up  into  short  bits  between  his  own  fingers.  He  had  not 
before  spoken.  Then  he  said,  ‘ Yes,  it  is  pliable,  and  it  does 

1 Experimental  Researches  in  Electricity , Vol.  IH,  p.  4. 

2 Darwin,  Cross  and  Self  Fertilization,  p.  374. 


246 


INDUCTIVE  LOGIC 


become  instantly  brittle.’  ” 1 Here  the  experiment  with  and 
without  the  significant  antecedent  and  consequent  indicates 
the  causal  relation,  especially  as  the  instantaneous  effect 
precludes  the  possibility  of  the  operation  of  any  other 
cause. 

Another  experiment  of  Faraday’s  is  that  of  his  investiga- 
tion of  the  behavior  of  Lycopodium  powder  on  a vibrating 
plate.  It  had  been  observed  that  the  minute  particles  of 
the  powder  collected  together  at  the  points  of  greatest  motion, 
whereas  sand  and  all  heavy  particles  collected  at  the  nodes, 
where  the  motion  was  least.  It  occurred  to  Faraday  to 
try  the  experiment  in  the  exhausted  receiver  of  an  air- 
pump,  and  it  was  then  found  that  the  light  powder  behaved 
exactly  like  heavy  powder.  The  inference  was  that  the 
presence  of  air  was  the  condition  of  importance,  because  it 
was  thrown  into  eddies  by  the  motion  of  the  plate,  and 
carried  the  Lycopodium  powder  to  the  points  of  greatest 
agitation.  Sand  was  too  heavy  to  be  carried  by  the  air.2 

Sir  John  Lubbock  gives  an  account  of  experiments  per- 
formed upon  insects  to  prove  that  the  sense  of  smell  is  in 
some  way  connected  with  their  antennae.  One  experiment 
was  performed  by  Forel,  who  removed  the  wings  from  some 
blue-bottle  flies  and  placed  them  near  a decaying  mole. 
They  immediately  walked  to  it,  and  began  licking  it  and 
laying  eggs.  He  then  took  them  away,  and  removed  the 
antennae,  all  other  circumstances  remaining  the  same  as 
before,  after  which,  even  when  placed  close  to  the  mole, 
they  did  not  appear  to  perceive  it.  Another  experiment 
similar  to  this  was  tried  by  Plateau,  who  put  some  food  of 
which  cockroaches  are  fond  on  a table  and  surrounded  it 
with  a low  circular  wall  of  cardboard.  He  then  put  some 
cockroaches  on  the  table ; they  evidently  scented  the  food, 
and  made  straight  for  it.  He  then  removed  their  antennae, 
after  which,  as  long  as  they  could  not  see  the  food,  they 

1 Gladstone,  Michael  Faraday,  p.  175. 

2 Jevons,  Principles  of  Science,  p.  419. 


THE  METHOD  OF  DIFEEEENCE 


247 


failed  to  find  it,  even  though  they  wandered  about  quite 
close  to  it.1 

Another  experiment  is  that  of  Graber  to  prove  the  sense 
of  hearing  in  insects.  He  placed  some  water-boatmen 
( Corixa ) in  a deep  jar  full  of  water,  at  the  bottom  of  which 
was  a layer  of  mud.  He  dropped  a stone  on  the  mud,  but 
the  beetles,  which  were  reposing  quietly  on  some  weeds, 
took  no  notice.  He  then  put  a piece  of  glass  on  the  mud, 
and  dropped  a stone  on  to  it,  thus  making  a noise,  though 
the  disturbance  of  the  water  was  the  same  as  when  the  stone 
was  dropped  on  the  mud.  The  water-boatmen,  however, 
then  at  once  took  flight.2 

An  illustration  of  the  method  of  difference  occurs  in  the 
so-called  blind  experiments,  which  are  often  made  in  chemistry 
especially.  As  Professor  Jevons  has  described  such  an 
experiment : “ Suppose,  for  instance,  a chemist  places  a 
certain  suspected  substance  in  Marsh’s  test  apparatus  and 
finds  that  it  gives  a small  deposit  of  metallic  arsenic,  he 
cannot  be  sure  that  the  arsenic  really  proceeds  from  the 
suspected  substance;  the  impurity  of  the  zinc  or  sulphuric 
acid  may  have  been  the  cause  of  its  appearance.  It  is 
therefore  the  practice  of  chemists  to  make  what  they  call 
blind  experiments,  that  is,  to  try  whether  arsenic  appears 
in  the  absence  of  the  suspected  substance.  The  same  pre- 
caution ought  to  be  taken  in  all  important  analytical 
operations.  Indeed  it  is  not  merely  a precaution,  it  is 
an  essential  part  of  any  experiment.  If  the  blind  trial  be 
not  made,  the  chemist  merely  assumes  that  he  knows  what 
would  happen.”3 

1 Lubbock,  On  the  Senses,  Instincts , and  Intelligence  of  Animals,  p.  45. 

2 Ibid.,  p.  75.  8 Jevons,  Principles  of  Science,  p.  433. 


CHAPTER  VIII 


THE  JOINT  METHOD  OF  AGREEMENT  AND  DIFFERENCE 

It  has  already  been  shown  that  the  method  of  difference 
is  sometimes  not  available,  inasmuch  as  it  may  be  neither 
possible  nor  practicable  to  remove  from  the  phenomenon  to 
be  investigated  the  suspected  causal  element  without  destroy- 
ing the  phenomenon  itself.  Sometimes,  too,  it  is  impossible 
even  to  neutralize  the  effect  of  the  causal  element  if  it  is 
allowed  to  remain  as  an  integral  part  of  the  phenomenon. 
This  is  especially  the  case  in  all  vital  phenomena,  and  also 
in  many  chemical  phenomena.  Therefore  another  method 
is  resorted  to,  which  is  known  as  the  joint  method  of  agree- 
ment and  difference.  Inasmuch  as  the  suspected  causal  ele- 
ment cannot  be  removed,  we  must  select  another  phenomenon 
as  much  like  the  former  as  possible,  which  is  however 
characterized  by  the  absence  of  the  causal  element.  By  the 
simple  method  of  difference,  two  instances  only  need  be 
compared,  the  one  with  and  the  other  without  the  causal 
element,  but  agreeing  precisely  in  every  other  particular. 
In  the  joint  method,  the  instances  with  and  without  the 
causal  element  differ,  it  may  be,  in  several  particulars.  A 
number  of  varying  instances  must  therefore  be  selected  so 
as  to  eliminate  the  possibility  of  any  of  these  differing  char- 
acteristics being  the  cause  in  question.  Therefore  two  sets 
of  instances  are  collected  and  compared.  The  one  set  com- 
prises all  the  positive  instances  having  the  presence  of  the 
supposed  causal  element,  and  the  second  set  consists  of  the 
negative  instances  having  the  supposed  causal  element  ab- 
sent altogether.  The  validity  of  the  method  depends  upon 
the  similarity  of  the  two  sets  of  instances.  As  the  similarity 

248 


AGREEMENT  AND  DIFFERENCE 


249 


increases,  the  method  approximates  to  the  simple  method 
of  difference. 

The  Canon  of  the  Joint  Method.  — If  several  instances  in 
which  the  phenomenon  occurs  have  only  one  circumstance 
in  common,  while  several  instances  in  which  it  does  not 
occur  have  nothing  in  common  save  the  absence  of  that  cir- 
cumstance; the  circumstance  in  which  alone  the  two  sets  of 
instances  differ,  is  the  effect,  or  cause,  or  a necessary  part 
of  the  cause,  of  the  phenomenon. 

The  symbolical  representation  of  this  method  may  be  ex- 
hibited as  follows,  using  a similar  notation  to  that  employed 
in  the  previous  methods  : — 


I.  Table  of  positive  instances. 

S + C 

+ e. 

S'  + c 

+ e. 

S"  + c 

. s" 

+ e. 

S'"  + c 

. s’" 

+ e. 

etc.  etc. 


II.  Table  of  negative  instances 

8, 

s„ 



etc. 

In  the  two  sets  of  instances,  the  following  conditions 
must  be  observed  in  order  to  render  the  method  valid : — 

1.  S + C,  S'  + C,  S"  + C,  S'"  + C,  etc., 

must  be  so  varied  that  they  reveal  but  one  constant  element, 
common  to  them  all,  as  C.  It  may  be  that  S will  resemble 
S'  in  more  marks  than  the  one,  namely  C,  and  this  may  be 
true  of  any  two  or  more  instances ; however,  taken  all  to- 
gether, they  must  possess  but  the  one  common  element  C. 

2.  In  the  same  way  St  may  resemble  Sn  in  more  marks 
than  merely  the  absence  of  C and  so  for  any  two  or  more 


sr 

sn. 

snr 

etc. 


250 


INDUCTIVE  LOGIC 


instances  in  the  series  St,  Su,  Sm,  etc.  However,  the  one 
characteristic  common  to  them  all  must  be  the  absence  of  C. 

3.  If  in  the  instances  chosen  an  element  is  common  to  all 
in  addition  to  C,  or  in  the  second  set  its  absence,  then  addi- 
tional instances  must  be  added  to  the  tables  both  positive 
and  negative  in  order  to  secure  this  all-important  condition 
of  elimination  through  suitable  variation. 

4.  Moreover,  the  two  series,  positive  and  negative,  must 
have  their  settings  similar.  S„  Su,  SIIP  etc.,  must  resemble 
S',  S",  S'",  etc. ; otherwise  the  negative  instances  would  not 
be  significant.1  They  must  be  chosen  from  the  same  sphere 
as  the  positive,  in  order  that  they  may  be  similar.  It  is 
possible  to  multiply  negative  instances  ad  infinitum,  which, 
however,  would  furnish  no  ground  for  any  inference,  be- 
cause they  would  be  wholly  irrelevant  to  the  problem  under 
investigation. 

5.  If  S,  is  so  similar  to  S'  as  to  be  identical  with  it,  and 
also  s,  passes  over  into  s';  then  we  have  the  method  of 
difference  in  its  pure  form:  — 

S'  + G s'  + e. 

S' s'. 

Here  the  setting,  instead  of  being  similar  in  the  two  cases, 
is  the  same  in  each. 

The  following  is  an  experiment  of  Sir  John  Lubbock’s 
concerning  the  sense  of  smell  in  insects,  which  I have  chosen 
as  illustrating  this  method  of  inductive  research.  He  took 
a large  ant  and  tethered  her  on  a board  by  a thread.  When 
she  was  quite  still,  he  brought  a tuning-fork  into  close 
proximity  to  her  antennae,  but  she  was  not  disturbed  in  the 
least.  He  then  approached  the  feather  of  a pen  very  quietly, 
so  as  almost  to  touch  first  one  and  then  the  other  of  the 
antennae,  which,  however,  did  not  move.  He  then  dipped 
the  pen  in  the  essence  of  musk  and  did  the  same;  the 
antenna  was  slowly  retracted  and  drawn  quite  back.  He 

1 See  p.  75. 


AGREEMENT  AND  DIFFERENCE 


251 


then  repeated  the  same  with  the  other  antenna,  and  with 
like  result.  Care  was  taken  throughout  not  to  touch  the 
antennae.  Lubbock  then  repeated  the  experiment  with  a 
number  of  different  ants,  and  using  various  substances. 
The  results  in  all  cases  were  the  same,  and  the  inference 
was  naturally  drawn  that  the  antennae  possessed  the  sense 
of  smell.  In  these  experiments  various  substances  were 
taken  having  nothing  in  common  save  the  odor  of  musk 
that  had  been  placed  upon  them. 

In  some  cases  it  is  not  possible  to  discover  positive  in- 
stances in  which  the  only  common  element  is  the  suspected 
cause.  In  such  cases  the  method  is  not  conclusive  in  its 
results,  although  it  may  attain  a high  degree  of  probability, 
if  all  the  common  elements  save  the  suspected  cause-element 
are  known  to  be  irrelevant,  or  can  in  any  other  way  be 
proved  to  have  no  influence  whatsoever  upon  the  result. 
Lor  instance,  an  illustration  is  often  given  of  this  method, 
which  fails  in  the  manner  just  described.  A man  is  attempt- 
ing to  discover  whether  a particular  article  of  food  disagrees 
with  him.  He  notices  several  occasions,  a large  number  if 
you  please,  when  he  has  eaten  this  particular  kind  of  food, 
and  has  soon  after  experienced  distress.  These  are  the  posi- 
tive instances.  This  peculiar  distress  has  never  been  ex- 
perienced when  he  has  abstained  from  the  food  in  question. 
The  inference  is  that  this  food  has  caused  the  distress.  In 
the  various  instances,  however,  the  sole  element  in  common 
is  not  merely  the  taking  or  not  taking  the  food.  The  per- 
son’s whole  bodily  organism  is  common  to  all  the  instances. 
Within  it,  unforeseen  complications,  independent  of  this 
article  of  food,  might  have  caused  the  trouble.  In  such 
cases  a large  number  of  instances  must  be  resorted  to  in 
order  to  render  the  possibility  of  a coincidence  out  of  the 
question. 

So  also  in  such  cases  as  the  treatment  of  any  given  disease 
in  a hospital.  An  experiment  may  be  tried  in  the  treat- 
ment, say,  of  typhoid  fever.  One  ward  may  be  subjected 


252 


INDUCTIVE  LOGIC 


to  a particular  kind  of  treatment,  and  another  ward  not  sub- 
jected to  that  treatment.  If  recovery  is  hastened  in  the  one 
and  retarded  in  the  other  case,  an  inference  may  be  drawn 
as  to  efficacy  of  this  treatment.  In  these  instances  again, 
while  they  are  all  different  patients,  still  the  nursing,  sur- 
roundings, etc.,  are  common  to  them  all.  It  must  be  shown 
that  these  are  present  both  in  the  negative  and  positive  in- 
stances, and  equally  capable  of  accomplishing  the  effect  if 
they  had  been  real  causes.  They  may  therefore  be  elimi- 
nated in  comparing  the  two  sets  of  instances,  because  com- 
mon both  to  the  negative  and  positive  cases.  In  this  also 
resort  must  be  had  to  the  number  of  instances  in  order  to 
eliminate  chance  coincidences.  The  presence  of  common 
elements  in  excess  of  the  common  causal  element  may  be 
represented  according  to  the  symbolical  notation  of  the  joint 
method,  by  the  introduction  of  another  symbol  x.  Let  x 
stand  for  that  which  is  common  to  all  instances  in  addition 
to  the  common  element  C.  We  then  have : — 

I.  Set  of  positive  instances. 

S + C + x 
S'  + C + x 
S"  + C + x 
S'"  + C +x 
etc. 

II.  Set  of  negative  instances. 

St  + x 
Su  + x 
Sin  + x 
etc. 

We  observe  x in  all  instances  both  positive  and  negative. 
Being  present  when  the  effect  occurs  and  when  it  does  not, 
indifferently,  we  can  at  once  infer  that  x is  not  the  whole 
cause  of  e.  However,  it  may  have  united  with  C in  the  first 


sr 

sir 

sur 

etc. 


s + e. 
s'  -f-  e. 
s"  + e. 
s'"  + e. 
etc. 


AGREEMENT  AND  DIFFERENCE 


253 


set  of  instances  to  produce  the  effect  e,  so  that  C without  x, 
or  some  part  or  parts  of  x,  could  not  alone  produce  the  effect 
e.  In  all  such  cases  the  exact  force  of  x must  be  estimated 
in  some  other  way.  If  x is  extremely  complex,  or  subject 
to  change  from  forces  emanating  from  within  itself,  as  in 
the  case  of  organic  phenomena,  then  it  becomes  extremely 
difficult  to  determine  x-,  and  consequently  the  method  of 
agreement  and  difference  does  not  yield  as  exact  results. 
As  long  as  the  force  of  x remains  unknown,  it  becomes  the 
source  of  possible  disturbance,  which  may  wholly  vitiate 
the  results  attained. 

Mr.  Darwin,  in  his  experiments  upon  cross  and  self  fer- 
tilization in  the  vegetable  kingdom,  placed  a net  about  one 
hundred  flower  heads,  thus  protecting  them  from  the  bees 
and  from  any  chance  of  fertilization  by  means  of  the  pollen 
conveyed  to  them  by  the  bees.  He  at  the  same  time  placed 
one  hundred  other  flower  heads  of  the  same  variety  of  plant 
where  they  would  be  exposed  to  the  bees,  and,  as  he  observed, 
were  repeatedly  visited  by  them.  Here  we  have  the  two 
sets  of  instances,  in  one  the  flowers  accessible  to  the  bees, 
and  in  the  other,  not  accessible.  He  obtained  the  following 
result.  The  protected  flowers  failed  to  yield  a single  seed. 
The  others  produced  68  grains’  weight  of  seed,  which  he 
estimated  as  numbering  2720  seeds.  Cross-fertilization  as 
the  cause  in  this  case  is  thus  proved.  The  common  element 
in  all  these  instances,  however,  is  not  merely  the  presence 
in  one  case  and  the  absence  in  the  other  of  the  bees ; there 
is  also  the  element  of  the  common  plant  structure  running 
through  all  of  the  two  hundred  instances.  This  element  is, 
however,  of  such  an  unvarying  nature  in  all  the  instances, 
and  the  number  observed  so  many  as  to  eliminate  the  possi- 
bility of  any  given  plant  structure  possessing  unobserved 
peculiarities  sufficient  to  produce  the  result  in  question.  It 
may  therefore  be  considered  as  an  inert  element  as  regards 
the  effects  noticed  in  the  one  and  absent  in  the  other  set  of 
instances. 


254 


INDUCTIVE  LOGIC 


Sir  John  Lubbock,  in  his  researches  concerning  the  dif- 
ferent functions  of  the  two  kinds  of  eyes  in  insects,  illus- 
trates the  joint  method  in  its  general  features.  The  two 
kinds  of  eyes  are  the  large  compound  eyes,  situated  one  on 
each  side  of  the  head,  and  the  ocelli,  or  small  eyes,  of  which 
there  are  generally  three,  arranged  in  a triangle  between  the 
other  two.  He  wished  to  determine  the  precise  function  of 
the  small  eyes,  the  ocelli ; and  he  has  gathered  together  the 
following  facts.  Plateau  has  shown  that  caterpillars,  which 
possess  ocelli,  but  no  compound  eyes,  are  very  short-sighted, 
not  seeing  above  one  to  two  centimetres.  He  has  also 
proved  by  experiments  that  spiders,  which  have  ocelli  but 
no  compound  eyes,  are  very  short-sighted;  they  were  easily 
deceived  by  artificial  flies  of  most  inartistic  construction, 
and  even  hunting  spiders  could  not  see  beyond  ten  centi- 
metres (four  inches).  Lubbock  experimented  on  this  point 
with  a female  spider,  which,  after  laying  her  eggs,  had 
rolled  them  into  a ball,  and  had  enveloped  the  whole  with  a 
silken  bag  which  she  carried  about  with  her.  Having  cap- 
tured the  female  and  having  taken  the  bag  of  eggs  from  her, 
he  placed  it  on  a table  about  two  inches  in  front  of  her. 
She  evidently  did  not  see  it.  He  then  pushed  it  gradually 
towards  her,  but  she  took  no  notice  till  it  nearly  touched 
her,  when  she  eagerly  seized  it.  He  then  took  it  away  a 
second  time,  and  put  it  in  the  middle  of  the  table,  which 
was  two  feet  four  inches  by  one  foot  four,  and  had  nothing 
else  on  it.  The  spider  wandered  about  for  an  hour  and 
fifty  minutes  before  she  found  it,  apparently  by  accident. 
He  then  took  it  away  again  and  put  it  down  as  before,  when 
she  wandered  about  for  an  hour  without  finding  it.  Like 
experiments  were  tried  with  other  spiders  and  with  the 
same  results.  Plateau  also  experimented  with  scorpions 
which  had  ocelli  and  no  compound  eyes.  They  appeared 
scarcely  to  see  beyond  their  own  pincers.  Moreover,  the 
ocelli  are  especially  developed  in  insects,  such  as  ants,  bees, 
aud  wasps,  which  live  partly  in  the  open  light  and  partly  in 


AGREEMENT  AND  DIFFERENCE 


255 


the  dark  recesses  of  nests.  Again,  the  night-flying  moths 
all  possess  ocelli.  On  the  other  hand,  however,  they  are 
entirely  absent  in  all  butterflies,  with  but  one  exception, 
according  to  Scudder,  namely,  the  genus  Pamphila.  Forel 
varnished  the  compound  eyes  of  various  insects  which 
had  ocelli  as  well.  The  latter  however  he  allowed  to 
remain  in  their  natural  state.  Inasmuch  as  their  habits 
of  flight  required  powers  of  vision  in  these  insects  extend- 
ing to  a considerable  distance,  it  happened  that  when  placed 
on  the  ground  they  made  no  attempt  to  rise;  while,  if 
thrown  into  the  air,  they  flew  first  in  one  direction  and  then 
in  another,  striking  against  any  object  that  came  in  their 
way,  and  being  apparently  quite  unable  to  guide  themselves. 
They  flew  repeatedly  against  a wall,  falling  to  the  ground, 
and  unable  to  alight  against  it,  as  they  did  so  cleverly  when 
they  had  their  compound  eyes  to  guide  them.  All  these 
instances,  taken  together  in  their  positive  and  negative 
aspects,  led  Sir  John  Lubbock  to  infer  that  the  ocelli  were 
useful  in  dark  places  and  for  near  vision,  while  the  com- 
pound eyes  were  for  the  light  and  more  distant  vision.1 

Another  illustration  of  this  method  may  be  found  in 
Darwin’s  account  of  the  extreme  tameness  of  the  birds  in 
the  Galapagos  and  Falkland  islands.  I quote  some  extracts 
from  his  narrative,  in  which  it  will  be  seen  that  Darwin’s 
inferences  follow  from  his  comparison  of  the  positive  and 
negative  instances  before  him.  He  says  : “ This  tameness 
of  disposition  is  common  to  all  the  terrestrial  species  of 
these  islands  in  the  Galapagos  Archipelago ; namely,  to  the 
mocking-thrushes,  the  finches,  wrens,  tyrant  flycatchers,  the 
dove,  and  carrion-buzzard.  All  of  them  often  approached 
sufficiently  near  to  be  killed  with  a switch,  and  sometimes, 
as  I myself  tried,  with  a cap  or  hat.  A gun  is  here  almost 
superfluous ; for,  with  the  muzzle,  I pushed  a hawk  off  the 
branch  of  a tree.  In  Charles  Island,  which  had  been  colo- 
nized about  six  years,  I saw  a boy  sitting  by  a well  with  a 
1 Lubbock,  On  the  Senses,  Instinct,  and  Intelligence  of  Animals,  pp.  175  ff. 


256 


INDUCTIVE  LOGIC 


switch  in  his  hand,  with  which  he  killed  the  doves  and 
finches  as  they  came  to  drink.  He  had  already  procured  a 
little  heap  of  them  for  his  dinner ; and  he  said  that  he  had 
constantly  been  in  the  habit  of  waiting  by  this  well  for  the 
same  purpose.  The  Falkland  Islands  offer  instances  of 
birds  with  a similar  disposition.  The  snipe,  upland  and 
lowland  goose,  thrush  bunting,  and  even  some  true  hawks, 
are  more  or  less  tame.  The  black-necked  swan  is  here  wild, 
and  it  was  impossible  to  kill  it.  It  however  is  a bird  of 
passage,  which  probably  brought  with  it  the  wisdom  learned 
in  foreign  countries. 

“ From  these  several  facts,  we  may,  I think,  conclude  that 
the  wildness  of  birds  with  regard  to  man  is  a particular 
instinct  directed  against  him  and  not  dependent  on  any 
general  degree  of  caution  arising  from  other  sources  of 
danger  ; secondly,  that  it  is  not  acquired  by  individual  birds 
in  a short  time,  even  when  much  persecuted,  but  that  in  the 
course  of  successive  generations  it  becomes  hereditary. 
With  domesticated  animals  we  are  accustomed  to  see  new 
mental  habits  or  instincts  acquired  and  rendered  hereditary, 
but  with  animals  in  a state  of  nature  it  must  always  be 
most  difficult  to  discover  instances  of  acquired  hereditary 
knowledge.  In  regard  to  the  wildness  of  birds  towards 
man,  there  is  no  way  of  accounting  for  it  except  as  an  in- 
herited habit;  comparatively  few  young  birds,  in  any  one 
year,  have  been  injured  by  man  in  England,  yet  almost  all, 
even  nestlings,  are  afraid  of  him;  many  individuals,  on  the 
other  hand,  both  at  Galapagos  and  at  the  Falklands,  have 
been  pursued  and  injured  by  him,  but  yet  have  not  learned 
a salutary  dread  of  him.”  1 

I have  given  this  quotation  somewhat  at  length  in  order 
to  show  the  method  of  a great  investigator  in  the  realm  of 
nature ; and  that  it  may  be  seen  how  naturally  he  falls  into 
the  method  of  comparing  positive  and  negative  sets  of  in- 
stances relative  to  the  object  of  research.  The  animal  and 
1 Darwin,  Voyage  of  a Naturalist,  Vol.  II,  pp.  172  f. 


AGREEMENT  AND  DIFFERENCE 


257 


vegetable  kingdoms  are  especially  adapted  to  the  applica- 
tion of  this  joint  method,  and  therefore  it  is  in  biology  that 
it  is  most  frequently  employed  and  where  it  has  yielded  the 
most  fertile  results. 

The  advantage  of  the  joint  method  over  the  simple 
method  of  agreement  is  that  it  largely  eliminates  the  possi- 
bility of  there  being  any  other  cause  of  the  given  phenome- 
non than  the  one  disclosed  by  the  operation  of  this  method. 
The  method  of  agreement,  as  we  have  seen,  often  fails  of  a 
definite  result  owing  to  the  plurality  of  causes.  The  joint 
method  tends  to  indicate  the  one  and  only  cause,  and  when 
the  instances  are  rigorously  selected  according  to  the  condi- 
tions of  the  canon,  there  is  a high  degree  of  probability  that 
the  sole  cause  is  discovered.  Mr.  Mill  at  this  point  claims 
too  much  for  the  method  in  insisting  that  it  gives  a certainty 
regarding  the  sole  cause,  when  the  requirements  are  perfectly 
realized.  It  is  impossible  to  realize  the  requirements  per- 
fectly. In  selecting  the  negative  instances,  we  are  never 
sure  that  we  have  compassed  the  entire  sphere  of  significant 
negative  instances.  We  may,  however,  attain  results  highly 
probable  in  this  regard,  though  they  may  not  reach  an  abso- 
lute certainty.  Such  a statement  is  more  moderate  in  its 
expression,  and  practically  it  assures  as  satisfactory  results. 


CHAPTER  IX 


THE  METHOD  OF  CONCOMITANT  VARIATIONS 

The  method  of  concomitant  variations  is  a process  of 
determining  a causal  relation  when,  as  an  element  in  an 
antecedent  varies  in  intensity  greater  or  less,  there  is 
observed  a corresponding  or  concomitant  variation  in  the 
consequent. 

Canon  of  the  Method  of  Concomitant  Variations.  — What- 
ever phenomenon  varies  in  any  manner,  whenever  another 
phenomenon  varies  in  some  particular,  is  either  a cause  or 
an  effect  of  that  phenomenon,  or  is  connected  with  it  through 
some  fact  of  causation. 

The  latter  clause  of  this  canon  provides  for  that  circum- 
stance in  which  the  varying  elements  may  both  be  con- 
comitant effects  of  a common  cause.  When  we  are  assured 
of  the  absence  of  any  possible  common  cause  to  which  we 
can  assign  the  two  phenomena  as  effects,  then  they  must 
be  related  between  themselves  as  cause  and  effect.  A 
simple  illustration  of  this  method  is  the  rise  of  the  mercury 
in  the  thermometer  owing  to  the  increase  of  heat ; its  fall, 
whenever  there  is  decrease  of  heat.  One  varies  as  the 
other  concomitantly,  and  we  infer  a causal  relation  that 
we  at  once  proceed  to  generalize  without  hesitation. 

The  symbolical  representation  of  this  method  is  as 
follows : — 


S + C . . . . 

S+C±dC  . . 


s + e. 
s + e ± de. 


etc. 

Then  C is  the  cause  of  e. 


etc. 


258 


CONCOMITANT  VARIATIONS 


259 


I have  used  dC  and  de  to  denote  the  increments  or 
decrements  of  the  cause  and  effect  respectively.  This 
method  is  used  generally  when  the  method  of  difference  is 
impossible,  owing  to  the  fact  that  the  supposed  causal 
element  cannot  be  made  to  vanish  wholly.  In  all  such 
cases  a variation  of  the  element  is  resorted  to,  and  the 
corresponding  result  observed.  Heat  is  relative  and  not 
absolute,  as  also  the  height  of  mercury  in  the  tube.  The 
relation  is  determined,  therefore,  by  variations,  greater  and 
less.  This  method  is  also  used  to  supplement  the  results 
of  other  methods  by  which  a causal  relation  has  been 
determined,  but  not  in  exact  quantitative  terms.  It  may 
be  known  that  a certain  phenomenon  C is  always  the  cause 
of  a certain  effect  e,  and  the  method  of  concomitant  vari- 
ations will  then  be  of  use  in  determining  precisely  how 
much  of  a variation  in  C will  cause  a specified  variation 
in  e.  A law  finds  scientific  expression  only  when  stated  in 
terms  of  exact  quantitative  relation  between  variations  in 
antecedent  and  consequent.  We  may  express  the  law  of 
universal  attraction  in  a vague  way  that  bodies  always 
attract  each  other,  and  the  greater  attraction  when  the 
bodies  are  nearer  together,  and  the  larger  they  are.  But 
this  statement  needs  to  be  recast  in  terms  exhibiting  the 
precise  quantitative  variation,  — bodies  attract  each  other 
directly  as  the  product  of  their  masses,  and  inversely  as  the 
square  of  their  distance.  It  is  evident  that  the  special 
function  of  this  method  of  concomitant  variations  consists 
in  just  this  quantitative  determination.  In  one  respect, 
therefore,  it  may  be  regarded  as  a substitute  for  the  method 
of  difference,  and  in  another  way  as  a supplement  to  the 
method  of  difference  in  leading  to  quantitatively  determi- 
nate results. 

The  quantitative  variation  between  antecedent  and  con- 
sequent may  be  either  direct  or  inverse  variation.  The 
former  is  when  one  increases  as  the  other  increases,  or 
when  one  decreases  as  the  other  decreases.  The  inverse  is 


260 


INDUCTIVE  LOGIC 


when  one  decreases  as  the  other  increases,  or  vice  versa. 
This  may  be  expressed  symbolically 

S -f-  G i dC  . . . . s + e T de. 


We  have,  for  instance,  Boyle’s  law  as  regards  the  variation 
of  volume  of  gases  according  to  the  pressure ; that  is, 
when  we  double  the  pressure,  we  halve  the  volume.  This 
may  be  proved  experimentally.  The  method  also  was 
used  by  Ricardo  to  prove  his  law  that  the  rate  of  profits 
varies  in  inverse  ratio  to  the  rate  of  wages.  We  have  also 
the  tendency  observed  in  respect  to  increase  of  crimes 
when  there  is  decrease  of  opportunities  for  labor. 

The  expression  of  a law  in  terms  of  the  quantitative 
relation  between  antecedent  and  consequent  may  be  facili- 
tated by  a graphic  representation  of  the  same,  through 
corresponding  abscissae  and  ordinates.  The  varying  ante- 
cedents, for  instance,  may  be  laid  off  on  the  axis  of  X, 
and  each  several  consequent  represented  by  the  corre- 
sponding ordinate.  The  resulting  curve  thus  obtained 
will  represent  the  law  of  their  mutual  relation.  If  the 
equation  of  the  curve  can  be  determined,  it  will  represent 
the  mathematically  exact  expression  of  the  law  in  ques- 
tion. If  this  is  not  possible,  it  may  prove  at  least  sug- 
gestive of  the  law  which  otherwise  might  have  remained 
concealed.  This  graphical  method  is  especially  useful  in 
dealing  with  physical  phenomena.  “If  the  abscissas  rep- 
resent intervals  of  time,  and  the  ordinates  corresponding 
heights  of  the  barometer,  we  may  construct  curves  which 
show  at  a glance  the  dependence  of  barometric  pressure 
upon  the  time  of  day.  Such  curves  may  be  accurately 
drawn  by  photographic  processes  on  a sheet  of  sensitive 
paper  placed  behind  the  mercurial  column,  and  made  to 
move  past  it  with  a uniform  horizontal  velocity  by  clock- 
work. A similar  process  is  applied  to  the  temperature  and 


CONCOMITANT  VARIATIONS 


261 


electricity  of  the  atmosphere,  and  to  the  components  of  ter- 
restrial magnetism.”  1 

The  method  of  concomitant  variation  has  the  advantage 
of  the  psychological  impression  which  it  makes.  The 
mind  is  more  susceptible  to  the  perception  of  variation  in 
forces  where  the  change  is  apparent  to  the  senses,  than  to 
the  perception  of  a constant  force,  whose  constaut  character 
thereby  conceals  its  nature  and  function  from  the  senses. 
Synchronous  changes  attract  the  attention,  and  admit  of 
ready  comparison,  as  we  follow  out  the  variations  from 
point  to  point.  We  may  ring  a bell  in  a vacuum,  and  detect 
no  sound  whatsoever,  and  then  allow  the  air  to  enter  gradu- 
ally. We  notice  that  as  the  air  enters  more  and  more  freely, 
the  sound  grows  louder  and  louder.  The  relation  of  cause 
and  effect  is  thus  demonstrated  to  the  senses  in  the  most 
vivid  manner  possible.  The  variations  are  exhibited  side 
by  side,  and  thus,  presented  together  in  their  concomitant 
relation,  produce  the  deeper  impression. 

This  method  is  of  special  advantage  in  all  experiments 
where  the  intensity  of  the  forces  can  be  varied  at  will  and 
the  consequent  effects  exhibited  in  some  palpable  manner. 
The  determination  of  the  heat  rays  in  the  solar  spectrum  is 
accomplished  by  this  method.  The  spectrum  may  be 
received  upon  a plate  pierced  with  a narrow  slit,  through 
which  the  rays  can  act  upon  a thermo-electric  pile,  which 
will  indicate  by  deflections  of  a needle  the  varying  intensity 
of  the  heat  in  the  several  rays  of  the  spectrum.  Now, 
move  the  slit  through  the  whole  extent  of  the  spectrum, 
beginning  with  the  violet  portion.  While  in  the  violet,  the 
indigo,  the  blue,  and  even  the  green,  the  needle  of  the  ther- 
moscopic  apparatus  will  be  deflected  but  slightly,  it  will 
indicate  an  amount  of  heat  increasing  as  the  slit  crosses  the 
yellow,  next  the  orange,  then  the  red ; and  then  beyond  the 
red,  and  entering  the  dark  portion  of  the  spectrum,  we  find 
the  greatest  deflection  of  all.  The  maximum  of  heat  is 

1 Thomson  and  Tait,  Elements  of  Natural  Philosophy,  Vol.  I,  p.  119. 


262 


INDUCTIVE  LOGIC 


therefore  in  a region  beyond  the  observation  of  the  senses 
when  unaided  by  experimental  device ; and  yet  revealed 
conclusively  by  this  method.1 

Professor  Tyndall  performed  a very  interesting  experi- 
ment to  prove  that  the  cloud  of  darkness  surrounding  flames 
of  great  heat  was  due  to  the  fact  that  the  heat  consumed 
the  floating  motes  in  the  air  which  serve  to  scatter  the  light 
which  is  visible  only  when  thus  diffused.  The  phenomenon 
which  he  endeavored  to  explain  was  somewhat  as  follows : 
Beneath  a beam  of  electric  light,  a red-hot  poker  was  placed, 
and  from  it  black  wreaths  as  of  smoke  were  seen  to  ascend. 
A large  hydrogen  flame  being  employed,  it  produced  whirl- 
ing masses  of  darkness  far  more  copiously  than  the  poker. 
Of  this  Professor  Tyndall  remarked : “ Smoke  was  out  of 
the  question  ; what  then  was  the  blackness  ? It  was  simply 
that  of  stellar  space ; that  is  to  say,  blackness  resulting  from 
the  absence  from  the  track  of  the  beam  of  all  matter  com- 
petent to  scatter  its  light.  When  the  flame  was  placed 
below  the  beam,  the  floating  matter  was  destroyed  in  situ  ; 
and  the  air  freed  from  this  matter  rose  into  the  beam,  jostled 
aside  the  illuminated  particles,  and  substituted  for  their 
light  the  darkness  due  to  its  own  perfect  transparency. 
Nothing  could  more  forcibly  illustrate  the  invisibility  of 
the  agent  which  renders  all  things  visible.  The  beam 
crossed,  unseen,  the  black  chasm  formed  by  the  transpar- 
ent air,  while  at  both  sides  of  the  gap  the  thick-strewn  par- 
ticles shone  out  like  a luminous  solid  under  the  powerful 
illumination.”  2 Such  being  the  phenomenon  and  Professor 
Tyndall’s  explanation,  it  will  be  seen  that  he  proceeded 
according  to  the  method  of  concomitant  variations  in  the 
following  experiment  of  many  which  he  performed  to  sub- 
stantiate this  theory : — 

A platinum  tube  with  its  plug  of  platinum  gauze  was 
connected  with  an  experimental  tube,  through  which  a pow- 

1 Saigey,  The  Unity  of  Natural  Phenomena,  p.  61. 

1 Tyndall,  Fragments  of  Science,  p.  280. 


CONCOMITANT  VARIATIONS 


263 


erful  beam  could  be  sent  from  an  electric  lamp  placed  at  its 
end.  The  platinum  tube  was  heated  till  it  glowed  feebly 
but  distinctly  in  the  dark.  The  experimental  tube  was 
then  exhausted,  and  filled  with  air  that  had  passed  through 
the  red-hot  tube.  A considerable  amount  of  floating  matter 
which  had  escaped  combustion  was  revealed  by  the  electric 
beam. 

Then  the  tube  was  raised  to  a brighter  redness  and  the 
air  permitted  to  pass  slowly  through  it.  Though  diminished 
in  quantity,  a certain  amount  of  floating  matter  passed  into 
the  exhausted  experimental  tube. 

The  platinum  tube  was  rendered  still  hotter;  a barely 
perceptible  trace  of  the  floating  matter  now  passed  through 
it.  The  experiment  was  repeated,  with  the  difference  that 
the  air  was  sent  more  slowly  through  the  red-hot  tube.  The 
floating  matter  was  totally  destroyed.  The  platinum  tube 
was  now  lowered  until  it  bordered  upon  a visible  red  heat. 
The  air,  sent  through  it  still  more  slowly  than  in  the  last 
experiment,  carried  with  it  a cloud  of  floating  matter.  Pro- 
fessor Tyndall’s  commentary  upon  this  experiment  is  as 
follows:  “If,  then,  the  suspended  matter  is  destroyed  by 
a bright  red  heat,  much  more  is  it  destroyed  by  a flame 
whose  temperature  is  vastly  higher  than  any  employed 
in  this  experiment.  So  that  the  blackness  introduced 
into  a luminous  beam  where  a flame  is  placed  beneath  it 
is  due,  as  stated,  to  the  destruction  of  the  suspended 
matter.” 1 

Professor  Tyndall  also  supplemented  this  experiment  by 
one  which  was  according  to  the  joint  method  of  agreement 
and  difference.  He  prepared  oxygen  so  as  to  exclude  all 
floating  particles,  and  found  that  when  blown  into  the  beam, 
darkness  was  produced ; also  that  hydrogen,  nitrogen,  car- 
bonic acid,  and  coal-gas,  when  prepared  in  a similar  way, 
each  produce  darkness  when  poured  or  blown  into  the  beam. 
These  instances,  combined  with  various  positive  instances  of 
1 Tyndall,  Fragments  of  Science , pp.  283,  284. 


264 


INDUCTIVE  LOGIC 


illumination  of  mote-strewn  currents  of  air,  illustrate  the 
method  of  agreement  and  difference. 

An  additional  experiment,  according  to  the  method  of 
difference,  wTas  as  follows : Professor  Tyndall  placed  an 
ordinary  glass  shade  in  the  air  with  its  mouth  downward. 
This  permitted  the  track  of  the  beam  to  be  seen  crossing  it. 
Letting  coal-gas,  or  hydrogen,  enter  the  shade  by  a tube 
reaching  to  its  top,  the  gas  gradually  filled  the  shade  from 
the  top  downward.  As  soon  as  it  occupied  the  space  crossed 
by  the  beam,  the  luminous  track  was  instantly  abolished. 
Lifting  the  shade  so  as  to  bring  the  common  boundary  of 
gas  and  air  above  the  beam,  the  track  flashed  forth.  After 
the  shade  was  full,  he  inverted  it ; thereupon  the  gas  passed 
upward  like  a black  smoke  among  the  illuminated  particles.1 

The  method  of  concomitant  variations  is  not  only  capable 
of  illustration  by  laboratory  methods  and  devices ; it  finds 
abundant  illustration  as  well  in  the  realm  of  nature,  where 
observation  alone  becomes  the  instrument  of  investigation 
and  where  experiment  is  impossible  or  impracticable.  Lyell, 
in  his  Principles  of  Geology,  gives  a very  interesting  account 
of  the  alternate  elevation  and  subsidence  of  the  temple  of 
Jupiter  Serapis,  at  Pozzuoli,  on  the  Bay  of  Naples.*  It  is 
situated  in  proximity  to  several  volcanoes,  Vesuvius,  however, 
being  at  some  distance.  It  has  been  observed  that  there  is 
a certain  connection  between  each  era  of  upheaval,  and  a 
local  development  of  volcanic  heat ; and  on  the  other  hand, 
between  each  era  of  depression,  and  the  local  quiescent  con- 
dition of  volcanic  phenomena.  Before  the  Christian  era, 
when  Ischia  was  in  a state  of  eruption,  and  Avernus  and 
other  points  in  the  Phlegraean  fields  were  celebrated  for  their 
volcanic  character,  it  was  observed  that  at  that  time  the 
ground  on  which  the  temple  stood  was  several  feet  above 
water.  Vesuvius  was  then  regarded  as  a spent  volcano. 
After  the  Christian  era,  Vesuvius  became  active  and  then 

1 Tyndall,  Fragments  of  Science,  pp.  284,  285. 

2 Chapter  XXX. 


CONCOMITANT  VARIATIONS 


265 


scarcely  a single  eruption  occurred  in  Ischia  or  around  the 
Bay  of  Bairn.  It  was  observed  that  at  that  time  the  temple 
was  sinking.  Vesuvius  then  became  quiet  for  five  centuries 
preceding  the  eruption  of  1631,  and  during  that  period  the 
Solfatara  was  in  eruption  in  1198,  Ischia  in  1302,  and  Monte 
Nuovo  was  formed  in  1538.  Then  the  foundations  of  the 
temple  were  observed  to  be  rising  again.  Vesuvius  became 
active  after  that,  and  has  continued  so  ever  since,  and  during 
this  time  the  temple  has  been  subsiding.  The  inference  is 
that  as  the  subterranean  heat  increases,  and  lava  forms 
without  obtaining  an  easy  vent  like  that  afforded  by  Vesu- 
vius, the  surface  is  elevated,  but  when  the  rocks  below  are 
cooling  and  contracting,  the  pent-up  fire  being  withdrawn 
in  the  eruption  of  the  great  Vesuvius,  then  there  is  a cor- 
responding subsidence. 

The  observation  of  concomitant  variations  is  furthermore 
illustrated  in  Darwin’s  researches  concerning  the  formation 
of  coral  reefs,  as  regards  the  question  which  some  natural- 
ists have  raised  as  to  which  part  of  the  coral  reef  is  most 
favorable  to  the  growth  of  coral.1  He  adduces  the  follow- 
ing facts,  most  of  which  are  the  direct  result  of  his  observa- 
tions : “ The  great  mounds  of  living  Porites  and  of  Millepora 
round  Keeling  atoll  occur  exclusively  on  the  extreme  verge 
of  the  reef,  which  is  washed  by  a constant  succession  of 
breakers.  At  the  Marshall  Islands  the  larger  kinds  of 
coral  which  form  rocks  measuring  several  fathoms  in  thick- 
ness prefer  the  most  violent  surf.  The  outer  margin  of  the 
Maldiva  atolls  consists  of  living  corals,  and  here  the  surf  is 
so  tremendous  that  even  large  ships  have  been  thrown,  by 
a single  heave  of  the  sea,  high  and  dry  on  the  reef,  all  on 
board  thus  escaping  with  their  lives.  In  the  Bed  Sea  the 
strongest  corals  live  on  the  outer  reefs  and  appear  to  love 
the  surf.  From  these  facts  it  is  certain  that  the  strongest 
and  most  massive  corals  flourish  where  most  exposed.  The 
less  perfect  state  of  the  reef  of  most  atolls  on  the  leeward 
1 Darwin,  Coral  Reefs,  pp.  87  f. 


266 


INDUCTIVE  LOGIC 


and  less  exposed  side,  compared  with  its  state  to  the  wind- 
ward, and  the  analogous  case  of  the  greater  number  of 
breaches  on  the  rear  sides  of  those  atolls  in  the  Maldiva 
Archipelago,  which  afford  some  protection  to  each  other, 
are  obviously  explained  by  this  circumstance.”  There 
seems  to  be  here  a combination  of  the  method  of  agreement 
with  that  of  concomitant  variations.  And  such  a combina- 
tion may  be  employed  to  advantage  in  cases  where  the  phe- 
nomena under  investigation  show  forces  under  varying 
degrees  of  intensity ; the  causal  relation  is  more  apparent, 
and  the  possibility  of  fortuitous  coincidence  is  largely  elimi- 
nated if  a number  of  instances  can  be  collected  in  which  the 
forces  manifest  themselves  in  varying  degrees.  Accumula- 
tion of  instances,  showing  concomitant  variations  in  the 
forces  observed,  corresponds  to  the  actual  variations  which 
in  an  experiment  are  effected  by  the  investigator  himself. 
In  such  observed  instances,  however,  we  cannot  always  have 
before  us  the  variations  expressed  continuously.  There 
are  evident  gaps  that  must  be  interpolated  mentally.  In 
experiment  however  of  whatever  nature,  the  degrees  of 
intensity  can  be  exhibited  continuously,  one  degree  merg- 
ing into  another  through  inappreciable  increments.  There 
is  thus  a gradation  which  has  no  gaps  to  be  filled,  and  the 
psychological  impression  is  thereby  heightened. 

By  the  method  of  concomitant  variations  it  is  possible  also 
to  represent  to  the  mind  the  magnitude  of  an  unknown  force, 
or  unobservable  force,  by  a comparison  with  the  intensity 
of  a known  force  which  lies  within  the  sphere  of  observa- 
tion. For  instance,  Mr.  Darwin  gives  an  interesting  account 
in  his  narrative  of  the  finding  near  the  shores  of  the  Plata 
a group  of  vitrified  siliceous  tubes  which  had  been  formed 
by  lightning  entering  loose  sand.  The  internal  surface  of 
such  tubes  is  completely  vitrified,  glossy,  and  smooth,  and 
the  tubes  themselves  are  generally  compressed,  and  have 
deep  longitudinal  furrows  so  as  closely  to  resemble  a 
shrivelled  vegetable  stalk,  or  the  bark  of  an  elm  or  cork 


CONCOMITANT  VARIATIONS 


267 


tree.  Their  circumference  is  about  two  inches,  but  in  some 
fragments  which  are  cylindrical  and  without  any  furrows, 
it  is  as  much  as  four  inches.  Judging  from  the  uncom- 
pressed fragments,  the  measure  or  bore  of  the  lightning 
proved  to  be  about  one  inch  and  a quarter.  In  contrast 
with  the  force  of  lightning  as  thus  revealed  in  its  effects, 
Mr.  Darwin  cites  some  experiments  performed  in  Paris  by 
an  artificial  force  of  great  magnitude  indeed  and  yet  with 
results  that  seem  insignificantly  small  in  comparison.  He 
says : “ At  Paris,  M.  Hatchette  and  M.  Beudant  succeeded 
in  making  tubes  in  most  respects  similar  to  these  fulgurites 
by  passing  very  strong  shocks  of  galvanism  through  finely 
powdered  glass : they  failed,  however,  both  with  powdered 
felspar  and  quartz.  One  tube,  formed  with  pounded  glass, 
was  very  near  an  inch  long,  namely,  .982,  and  had  an  inter- 
nal diameter  of  .019  of  an  inch.  When  we  hear  that  the 
strongest  battery  in  Paris  was  used,  and  that  its  power  on 
a substance  of  such  easy  fusibility  as  glass  was  to  form 
tubes  so  diminutive,  we  must  feel  greatly  astonished  at  the 
force  of  a shock  of  lightning,  which,  striking  the  sand  in 
several  places,  has  formed  cylinders  in  one  instance  at  least 
thirty  feet  long,  and  having  an  internal  bore,  where  not 
compressed,  of  full  an  inch  and  a half ; and  this  in  a mate- 
rial so  extraordinarily  refractory  as  quartz ! ” 1 

The  method  of  concomitant  variations  may  be  used  in 
regard  to  phenomena  whose  nature  is  such  as  seemingly  to 
indicate  a constant  law  of  variation,  and  yet  inferences 
based  thereupon  lead  to  false  results.  It  is  therefore  well 
to  note  some  of  these  instances  by  way  of  general  precaution 
in  applying  this  method. 

1.  It  does  not  necessarily  follow  that  having  observed 
two  forces  varying  in  a constant  ratio  through  several  con- 
comitant modifications,  the  same  ratio  will  be  preserved 
indefinitely  through  all  subsequent  changes.  Water  con- 
tracts as  it  is  cooling.  Suppose  we  begin  to  note  this  con- 
1 Darwin,  Voyage  of  a Naturalist,  Vol.  I,  pp.  76  f. 


268 


INDUCTIVE  LOGIC 


tinued  contracting  of  water  from  100°  F.  to  90°  ; we 
naturally  expect  to  find  it  continuing  through  90°  to  80°. 
And  as  we  observe,  we  find  our  expectations  confirmed. 
And  so  on  through  to  40°,  we  find  that  water  continues  to 
contract.  It  is,  therefore,  most  natural  for  us  to  expect  to 
find  water  contracting  at  39°.  But  just  at  this  point  in  the 
series,  there  is  a break  in  the  continuity  of  variation;  at 
39°  water  begins  to  expand  and  so  continues  until  it  passes 
into  the  solid  form  at  the  freezing-point.  The  same  also  is 
illustrated  in  Weber’s  law,  already  mentioned,  which  ex- 
presses the  quantitative  relation  between  the  stimulus  and 
the  corresponding  sensation.  The  law  is  that  the  force  of 
the  stimulus  must  increase  geometrically,  in  order  that  the 
intensity  of  the  sensation  should  increase  arithmetically. 
This  law,  however,  breaks  down  towards  the  upper  or 
lower  limits,  with  a stimulus  of  slight  degree  of  intensity 
and  with  one  of  extreme  intensity.  We  find  also  an  in- 
crease of  temperature  as  we  proceed  towards  the  centre  of  the 
earth  of  about  one  degree  to  every  fifty-three  feet  of  descent. 
This  by  no  means  warrants  us  in  inferring  that  this  ratio 
continues  constant  to  the  very  centre  itself.  In  certain 
phenomena,  moreover,  there  are  natural  limits,  as  in  sound, 
for  example,  where  the  pitch  rises  as  the  number  of  vibra- 
tions increases.  At  a certain  point,  varying  according  to 
different  individuals,  increase  of  vibrations  gives  no  result- 
ing sound  whatsoever ; and  so  there  is  a lower  limit,  — vibra- 
tions may  decrease  to  a point  beyond  which  no  sound  is 
heard. 

An  illustration  of  this  fallacy,  though  not  strictly  of  the 
method  of  concomitant  variations,  is  given  by  Jevons.  He 
takes  the  following  series  of  prime  numbers  : 41,  43,  47,  53, 
61,  71,  83,  97,  113,  131,  etc.  It  will  be  seen  that  they  all 
agree  in  being  values  of  the  general  expression  x2  -f-  x -f  41, 
where  we  put  for  x the  successive  values  of  0, 1,  2,  3,  4,  etc. 
For  instance,  let  x = 0 in  x2  + x + 41,  we  get  41 ; let  x = 1 
in  the  same,  we  get  43 ; when  x = 2,  we  get  47 ; and  so  on. 


CONCOMITANT  VARIATIONS 


269 


It  seems  as  though  we  could  keep  this  up  indefinitely,  pro- 
ducing an  increasing  series,  always  of  prime  numbers.  It 
is  found,  however,  that  if  we  take  x = 40,  in  the  formula 
x2  -f  x + 41,  we  shall  have  40  x 40  + 40  4-  41,  which  equals 
1681,  and  this  number  is  the  square  of  41  and  therefore  not 
a prime  number.  At  this  point  the  law  breaks  down.1 

In  the  sphere  of  political  economy  also  we  might  be  led 
into  an  easy  yet  false  inference.  Suppose  a certain  farm 
yield  500  bushels  of  com  with  a given  amount  of  expendi- 
ture and  labor.  We  might  think  that  if  we  double  the 
expenditure  and  labor,  we  will  also  be  able  to  double  the 
results,  and  obtain  a yield  of  1000  bushels  as  over  against 
the  500  of  the  previous  year.  Here,  however,  what  is 
known  as  the  law  of  decreasing  returns  obtains ; to  double 
the  product  it  may  be  necessary  to  triple  or  quadruple 
the  labor  and  expense.  “ Thus  in  the  production  of  any 
plot  of  land  there  is  a point  of  equilibrium,  which  marks 
an  impassable  limit,  not  of  course  a limit  which  could 
not  be  passed  if  it  were  wished,  but  one  that  no  one 
wishes  to  pass,  because  there  is  nothing  to  be  gained  by  so 
doing.” 2 

To  know  that  such  false  inferences  are  at  least  possible 
in  the  application  of  this  method  of  concomitant  variations 
to  the  unknown  regions  beyond  our  experience,  may  serve 
at  least  to  keep  us  on  guard  under  similar  circumstances. 

2.  There  are  certain  phenomena  moreover  in  which  an 
increased  intensity  of  the  force  in  question  may  give  rise  to 
incidental  effects  which  tend  to  neutralize  the  chief  effect  to 
be  attained.  For  instance,  an  overdose  of  arsenic  causes 
violent  contractions  of  the  stomach  so  that  its  contents  are 
immediately  ejected,  and  thus  the  system  is  relieved  of  the 
noxious  substance. 

3.  Two  elements  in  a given  phenomenon  may  vary  to- 
gether constantly  and  yet  they  may  not  be  related  at  all  as 

1 Jevons,  Principles  of  Science,  p.  230. 

3 Gide,  Political  Economy,  p.  325. 


270 


INDUCTIVE  LOGIC 


cause  and  effect,  but  appear  as  coincidental  effects  of  one 
and  the  same  cause.  It  has  been  observed  that  the  occur- 
rence of  the  aurora  borealis  has  been  accompanied  by  pro- 
nounced magnetic  disturbances.  It,  however,  cannot  be 
inferred  that  the  former  has  been  the  cause  of  the  latter ; 
they  are  probably  the  varied  effects  of  some  widely  operat- 
ing magnetic  force. 

The  precaution  above  mentioned  has  already  been  referred 
to  as  provided  for  in  the  canon  of  this  method  which  states 
that  the  observed  concomitant  variation  may  indicate  not 
always  a direct  causal  element  between  the  two  varying 
elements,  but  that  they  are  at  least  connected  with  the  phe- 
nomenon under  investigation  through  some  fact  of  causation. 


CHAPTER  X 


THE  METHOD  OF  EESIDUES 

The  method  of  residues  consists  in  the  analysis  of  a given 
phenomenon  based  upon  previous  inductions,  through  which 
it  has  been  determined  that  certain  elements  in  the  antece- 
dent have  caused  certain  elements  in  the  consequent ; the 
inference  is  then  drawn,  that  the  remaining  elements  of  the 
antecedent  are  necessarily  the  cause  of  the  remainder  of 
the  consequent.  It  is  a method  of  elimination  of  the  known 
relations  so  as  to  simplify  the  complex  character  of  the  phe- 
nomenon and  disclose  the  relations  that  are  unknown  in  the 
light  of  a causal  connection  which  we  are  constrained  to 
believe  must  obtain. 

The  Canon  of  the  Method  of  Residues.  — Subduct  from 
any  phenomenon  such  part  as  is  known  by  previous  induc- 
tions to  be  the  effect  of  certain  antecedents,  and  the  residue 
of  the  phenomenon  is  the  effect  of  the  remaining  antecedents. 

The  symbolical  representation  is  as  follows : — 

Given  S + C s + e. 

If  it  is  known  that  there  exists  already  the  causal  relation 
S s, 

we  may  then  infer  that  C is  the  cause  of  e.  In  this,  C may 
be  simple  or  complex ; if  it  is  simple,  the  causal  relation 
established  is  expressed  in  its  simplest  terms  and  is  there- 
fore a determinate  result.  If  however  the  residue  C is 
complex,  it  must  be  reduced  by  experimental  analysis  to  its 
simplest  elements,  and  their  relation  to  the  elements  into 
which  e can  be  analyzed  further  determined. 

271 


272 


INDUCTIVE  LOGIC 


The  most  striking  illustration  of  this  method,  and  one 
of  the  most  brilliant  achievements  of  science  as  well,  is  the 
discovery  of  the  planet  Neptune  by  Adams  and  Le  Verrier, 
working  on  the  problem  independently  and  reaching  the 
same  result.  These  astronomers  had  observed  certain  per- 
turbations in  the  planet  Uranus.  It  did  not  keep  in  its 
proper  orbit  as  determined  by  their  mathematical  calcula- 
tions based  upon  the  presence  of  the  known  stellar  bodies. 
It  behaved  as  though  beyond  its  orbit  was  an  outer  planet, 
whose  presence  alone  could  account  for  the  observed  per- 
turbations. Adams  and  Le  Verrier  then  proceeded  to  calcu- 
late the  exact  position  of  such  a disturbing  body  as  determined 
by  the  nature  and  magnitude  of  the  perturbations  of  Uranus. 
The  telescope  was  then  pointed  to  the  exact  point  in  the 
heavens,  as  thus  indicated,  and  the  planet  Neptune  was 
revealed  to  the  eye  according  to  the  determination  of  far- 
reaching  prophecy,  which  confidently  asserted  that  it  must 
be  there. 

The  method  of  residues  is  really  a deductive  method 
based  upon  the  law  of  sufficient  reason  ; so  many  elements 
on  the  one  hand  producing  so  many  elements  on  the  other ; 
if,  then,  a part  of  the  former  can  be  checked  off  as  cause  of 
a part  of  the  latter,  then  the  remainder  on  the  one  hand 
must  be  the  cause  of  the  remainder  on  the  other.  This  is 
pure  deduction.  For  we  ask,  Why  are  we  constrained  to 
account  for  the  remainder  on  one  side  by  the  remainder 
on  the  other  ? The  only  possible  answer  is  that  it  must  be 
accounted  for  within  the  system  to  which  it  is  referred ; 
and  but  one  part  therein  is  left  which  can  possibly  account 
for  it,  because  all  the  others  are  specifically  determined  in 
the  known  effects  which  they  have  produced.  This  method, 
however,  has  a proper  place  among  the  inductive  methods, 
inasmuch  as  it  is  based  on  previous  inductions,  and  leads 
to  investigations  that  can  be  prosecuted  only  by  the  various 
inductive  processes  of  experiment. 

When  the  residue  of  the  antecedent  is  a simple  element, 


THE  METHOD  OF  RESIDUES 


273 


and  no  other  possible  causal  clement  can  lie  concealed  from 
our  observation,  then  the  inference  is  simple  and  conclusive. 
A difficulty,  however,  may  present  itself,  owing  to  the  fact 
that  the  residual  element  is  apt  to  be  complex  and  leave  the 
phenomenon  still  indeterminate,  or  there  may  be  a lurking 
element  unnoticed  by  us  which  is  the  real  cause  in  question. 
The  function  of  this  method  is,  therefore,  largely  suggestive. 
It  says  the  effect  is  not  wholly  accounted  for  by  the  known 
causal  elements ; there  is  a residue  unaccounted  for,  and  its 
cause  is  to  be  sought  in  the  residue  of  the  antecedent,  and 
if  it  is  thought  that  the  whole  of  the  antecedent  is  compre- 
hended, the  question  is  started,  May  there  not  be  unobserved 
circumstances  of  the  antecedent  that  further  experiment 
will  be  calculated  to  reveal  ? In  many  cases,  therefore,  this 
method  must  be  supplemented  by  some  other  experimental 
method  in  order  to  secure  more  precise  determination,  gen- 
erally the  method  of  difference.  It  often  happens  in  inves- 
tigations in  chemistry,  astronomy,  and  physics,  that  the 
actual  phenomena  vary  in  greater  or  less  degree  from  their 
expected  behavior  according  to  established  theory.  This 
must  lead  either  to  a reconstruction  of  theory,  or  to  a search 
for  some  unobserved  force  sufficient  to  account  for  the  dis- 
crepancy. Herschel  was  the  first  to  point  out  the  signifi- 
cance of  such  discrepancies  in  scientific  research,  and  he 
called  them  residual  phenomena. 

An  illustration  of  such  a situation  and  the  solution  of  the 
problem  thus  presented  is  that  of  Sir  Humphry  Davy’s  ex- 
periments upon  the  decomposition  of  water  by  galvanism. 
“ He  found  that  besides  the  two  components  of  water,  oxy- 
gen and  hydrogen,  an  acid  and  alkali  were  developed  at  the 
two  opposite  poles  of  the  machine.  As  the  theory  of  the 
analysis  of  water  did  not  give  reason  to  expect  these  products, 
they  were  a residual  phenomenon,  the  cause  of  which  was  still 
to  be  found.  The  insight  of  Davy  conjectured  that  there 
might  be  some  hidden  cause  of  this  portion  of  the  effect ; the 
glass  containing  the  water  might  suffer  partial  decomposition, 


274 


INDUCTIVE  LOGIC 


or  some  foreign  matter  might  be  mingled  with  the  water,  and 
the  acid  and  alkali  be  disengaged  from  it,  so  that  the  water 
would  have  no  share  in  their  production.  Assuming  this, 
he  proceeded  to  try  whether  the  total  removal  of  the  cause 
would  destroy  the  effect  produced.  By  the  substitution  of 
gold  vessels  for  the  glass,  without  any  change  in  the  effect, 
he  at  once  determined  that  the  glass  was  not  the  cause. 
Employing  distilled  water,  he  found  a marked  diminution 
of  the  quantity  of  acid  and  alkali  evolved ; yet  there  was 
enough  to  show  that  the  cause,  whatever  it  was,  was  still  in 
operation.  The  impurity  of  the  water,  then,  was  not  the 
sole,  but  a concurrent,  cause.  He  now  conceived  that  the 
perspiration  from  the  hands  touching  the  instruments  might 
affect  the  case,  as  it  would  contain  common  salt,  and  an 
acid  and  alkali  would  result  from  its  decomposition  under 
the  agency  of  electricity.  By  carefully  avoiding  such  con- 
tact, he  reduced  the  quantity  of  the  products  still  further, 
until  no  more  than  slight  traces  of  them  were  perceptible. 
What  remained  of  the  effect  might  be  traceable  to  impuri- 
ties of  the  atmosphere  decomposed  by  contact  with  the 
electrical  apparatus.  An  experiment  determined  this ; the 
machine  was  placed  under  an  exhausted  receiver,  and  when 
thus  secured  from  atmospheric  influence,  it  no  longer  evolved 
the  acid  and  alkali.”1 

By  means  of  the  suggestions  incident  upon  this  method, 
Bunsen,  in  1860,  discovered  two  new  alkaline  metals,  cae- 
sium and  rubidium.  He  was  examining  alkalies  produced 
by  the  evaporation  of  mineral  water  from  Durkheim.  The 
flame  of  these  salts  was  examined  by  the  spectroscope. 
Bunsen  discovered  several  bright  lines  which  he  had  never 
noticed  before,  and  which  he  knew  could  not  be  produced 
by  potash  or  soda,  whose  corresponding  lines  were  in  close 
proximity.  He  then  subjected  the  mixture  to  a searching 
analysis  and  succeeded  in  obtaining  two  new  alkaline  sub- 
stances. When  he  had  separated  them,  he  then  tested  them 
iGore,  The  Art  of  Scientific  Discovery,  pp.  432,  433. 


THE  METHOD  OF  RESIDUES 


275 


by  the  method  of  difference,  by  which  he  found  that 
they  were  capable  of  producing  the  lines  at  first  no- 
ticed ; but  when  withdrawn,  the  lines  instantaneously  dis- 
appeared. 

Thomson  and  Tait,  in  their  Elements  of  Natural  Philoso- 
phy, have  the  following  reference  and  illustration  of  this 
method.  “ When,  in  an  experiment,  all  known  causes  being 
allowed  for,  there  remain  unexplained  effects  (excessively 
slight  it  may  be),  these  must  be  carefully  investigated,  and 
every  conceivable  variation  of  arrangement  of  apparatus, 
etc.,  tried ; until,  if  possible,  we  manage  so  to  exaggerate 
the  residual  phenomenon  as  to  be  able  to  detect  its  cause. 
It  is  here  perhaps  that  in  the  present  state  of  science  we 
may  most  reasonably  look  for  extensions  of  our  knowledge ; 
at  all  events,  we  are  warranted  by  the  recent  history  of 
natural  philosophy  in  so  doing.  Thus,  to  take  only  a very 
few  instances,  and  to  say  nothing  of  the  discovery  of  elec- 
tricity and  magnetism  by  the  ancients,  the  peculiar  smell 
observed  in  a room  in  which  an  electrical  machine  is  kept  in 
action  was  long  ago  observed,  but  called  the  ‘ smell  of  elec- 
tricity,’ and  thus  left  unexplained.  The  sagacity  of  Schon- 
bein  led  to  the  discovery  that  this  is  due  to  the  formation 
of  ozone,  a most  extraordinary  body,  of  enormous  chemical 
energies ; whose  nature  is  still  uncertain,  though  the  atten- 
tion of  chemists  has  for  years  been  directed  to  it.” 1 

Another  illustration  of  this  method  is  seen  in  the  com- 
parison of  the  observed  and  calculated  positions  of  Encke’s 
comet.  It  was  found  that  the  comet  returned  a little  sooner 
than  it  should  have  done,  the  period  regularly  decreasing 
from  1212.79  days,  between  1786  and  1789,  to  1210.44 
between  1855  and  1858.  The  inference  has  been  that  there 
is  a resisting  medium,  as  the  ether,  filling  the  space  through 
which  the  comet  passes.  What  the  resisting  medium  is, 
and  its  nature,  is  of  course  a matter  of  conjecture  as  far  as 
revealed  by  this  method  alone.  The  method  merely  indi- 
1 Thomson  and  Tait,  Elements  of  Natural  Philosophy , Vol.  I,  pp.  113  f. 


276 


INDUCTIVE  LOGIC 


cates  some  resisting  medium  to  account  for  the  observed 
discrepancy.1 

Herschel  has  observed  that  all  great  astronomical  discov- 
eries have  been  disclosed  in  the  form  of  residual  differences. 
The  practice  was  introduced  by  Halley,  when  astronomer 
royal,  of  comparing  systematically  the  positions  of  the 
heavenly  bodies  as  actually  observed  with  what  might  have 
been  expected  theoretically.  His  reductions  of  the  lunar 
observations  gave  a series  of  residual  errors,  extending  from 
1722  to  1769.  These  were  carefully  tabulated,  and  formed 
the  basis  for  certain  modifications  of  the  lunar  theory.2 

A discrepancy  was  observed  by  Newton  between  the 
theoretical  and  actual  velocity  of  sound;  the  former  being 
968  feet  per  second,  and  the  latter  1142.  Newton’s  experi- 
ments and  calculation  were  both  inaccurate ; nevertheless, 
a real  discrepancy  has  been  proved  to  exist,  the  theoretical 
being  916  and  the  real  velocity  1090  feet  per  second.  In 
1816  La  Place  showed  this  difference  to  be  due  to  the  heat 
evolved  by  the  sudden  compression  of  the  air  during  the 
propagation  of  the  sound  wave,  the  heat  having  the  effect 
of  increasing  the  elasticity  of  the  air,  and  therefore  appre- 
ciably accelerating  the  sound  impulse. 

It  sometimes  happens  that  in  repeating  an  experiment, 
we  are  confronted  with  evidently  different  results.  Then, 
we  may  be  sure,  the  experiment  has  been  carelessly  or  inac- 
curately performed;  or  else  there  are  some  disturbing  causes 
not  observed  by  us.  On  the  other  hand,  however,  if  there 
is  no  likelihood  of  coincidence  on  repeated  trials,  yet,  never- 
theless, a marked  agreement  is  noticed  in  the  results  of  vari- 
ous trials,  the  mind  should  be  at  once  alert  to  discover  the 
hidden  cause  of  such  agreement,  and  possibly  may  be  led 
to  new  truths  of  great  importance.  The  following  illustra- 
tion is  given  by  Thomson  and  Tait : “With  a very  good 
achromatic  telescope  a star  appears  to  have  a sensible  disc. 
But,  as  it  is  observed  that  the  discs  of  all  stars  appear  to 
1 Jevons,  Principles  of  Science,  p.  570.  2 Ibid.,  p.  572. 


THE  METHOD  OF  RESIDUES 


277 


be  of  equal  angular  diameter,  we  of  course  suspect  some 
common  error.  Limiting  the  aperture  of  the  object-glass 
increases  the  appearance  in  question,  which,  on  full  investi- 
gation, is  found  to  have  nothing  to  do  with  discs  at  all.  It 
is,  in  fact,  a phenomenon  due  to  diffraction  of  light.”  1 

It  was  said  of  Darwin  that  in  his  researches  the  residual 
phenomena  were  always  the  special  objects  of  his  attention. 
His  son,  Francis  Darwin,  says  of  him:  “There  was  one 
quality  of  mind  which  seemed  to  be  of  special  and  extreme 
advantage  in  leading  him  to  make  discoveries.  It  was  the 
power  of  never  letting  exceptions  pass  unnoticed.  Every- 
body notices  a fact  as  an  exception  when  it  is  striking  or 
frequent,  but  he  had  a special  instinct  for  arresting  an  ex- 
ception. A point  apparently  slight  and  unconnected  with 
his  present  work  is  passed  over  by  many  a man  almost 
unconsciously,  with  some  half-considered  explanation,  which 
is  in  fact  no  explanation.  It  was  just  these  things  that  he 
seized  upon  to  make  a start  from.  In  a certain  sense  there 
is  nothing  special  in  this  procedure,  many  discoveries  being 
made  by  means  of  it.  I only  mention  it,  because,  as  I 
watched  him  at  his  work,  the  value  of  this  power  to  an 
experimenter  was  so  strongly  impressed  upon  me.” 2 This 
is  striking  testimony  as  to  the  practical  worth  of  this 
method  as  an  instrument  of  research. 

This  method  has  also  been  applied  to  the  more  practical 
usage  of  examining  the  refuse  of  manufactured  and  other 
products  in  order  to  discover  some  concealed  utility.  The 
analysis  of  coal-tar  refuse  has  led  to  the  discovery  of  many 
valuable  substances  that  have  proved  of  use’  in  the  arts,  and 
in  medicine  as  well.  Glauber,  the  eminent  chemist,  and  a 
discoverer  of  several  chemical  compounds,  said  he  made  it 
a rule  to  examine  what  every  other  chemist  threw  away. 

1 Thomson  and  Tait,  Elements  of  Natural  Philosophy , Vol.  I,  p.  114. 

2 F.  Darwin,  Life  and  Letters  of  Charles  Darwin,  Vol.  I,  p.  125. 


CHAPTER  XI 


PREDICTION  AND  VERIFICATION 

When  our  inductive  methods  have  finally  led  us  to  for- 
mulate some  universal  law  or  principle,  we  are  then  able  to 
use  the  same  as  a major  premise  upon  which  to  ground  fur- 
ther deductions,  and  so  to  apply  the  results  of  inductive 
research  to  new  fields  not  as  yet  investigated.  Mr.  Mill 
calls  this  procedure  the  deductive  method  of  reasoning. 
Inasmuch  however  as  it  is  founded  upon  some  previous 
induction,  it  would  seem  more  fitting  to  designate  it  as  the 
inducto-deductive  method.  It  is  essentially  a combined 
process  of  induction  and  deduction.1  This  so-called  inducto- 
deductive  method  consists  of  three  stages  as  follows : — 

1.  Obtaining  by  the  inductive  methods  already  described, 
the  evidence  of  some  existing  causal  connection,  tentatively 
expressed  in  the  form  of  a universal  law. 

2.  Regarding  this  universal  law  as  the  basis  for  subse- 
quent deductions,  by  which  we  gain  a knowledge  of  the 
nature  of  unknown  phenomena,  as  necessitated  by  the  con- 
ditions of  this  law. 

3.  Verifying  the  results  thus  obtained  by  their  corre- 
spondence with  the  phenomena  as  actually  observed.  Where 
this  correspondence  is  wanting,  then  either  the  law  has 
not  been  correctly  expressed,  or  there  must  have  been  some 
error  in  our  deduction  based  upon  it.  When  we  are  assured 
that  the  latter  is  not  the  case,  then  a discrepancy  between 
the  theoretically  deduced  result  and  the  actual  facts  as 
observed,  always  discredits  our  original  induction.  This 

1 See  pp.  171  f. 

278 


PREDICTION  AND  VERIFICATION 


279 


method  of  verification  serves  as  a check  upon  hasty  general- 
ization, on  the  one  hand ; and  on  the  other,  it  serves  to  ex- 
tend our  knowledge  into  unknown  regions,  and  is  valuable 
as  a means  of  scientific  prediction.  In  the  development  of 
scientific  knowledge,  it  has  been  a potent  factor  in  enlarg- 
ing the  bounds  of  knowledge  beyond  the  sphere  of  imme- 
diate observation. 

This  combined  process  of  reasoning  is  the  one  commonly 
employed  by  us  all.  Induction  and  deduction  are  not  sep- 
arate processes,  but,  as  before  remarked,  they  are  comple- 
mentary factors  in  the  one  actual  process  of  reasoning.  We 
are  continually  using  our  inductions  as  a deductive  basis, 
inferring  how  things  should  be  before  they  are  really  seen ; 
and,  when  seen,  at  once  instinctively  comparing  prior  in- 
ference with  preseut  fact,  we  are  either  confirmed  in  our 
reasoning  process,  or  compelled  to  discard  our  previous  in- 
ference as  false  or  inadequate  as  the  case  may  be.  Our 
world,  the  world  of  knowledge,  is  built  up  of  the  seen,  and 
the  unseen  as  well,  because  necessitated  by  inferences  grow- 
ing out  of  the  seen  which  we  are  constrained  to  make;  the 
unseen  which  we  thus  are  continually  building  into  the 
seen  and  regarding  it  as  though  the  actually  known,  we  are 
however  from  time  to  time  compelled  to  alter,  and  here  and 
there  tear  down  w'hat  we  have  too  rashly  builded,  as  the 
structure  is  put  to  the  test  of  verifying  fact. 

This  method  of  prediction  and  verification  was  used  to 
decide  between  inferences  drawn  by  Newton  and  Huyghens 
respective^,  regarding  the  nature  of  light.  Newton’s  ob- 
servations led  him  to  infer  that  light  consisted  of  particles 
of  matter  shot  out  from  the  sun.  Huyghens  insisted  that 
light  consisted  in  the  propagation  of  some  kind  of  disturb- 
ance in  the  manner  of  a wave-motion.  Newton’s  theory 
being  taken  as  established,  it  would  necessitate  that  light 
on  entering  a denser  body  of  water,  being  refracted  more 
nearly  in  a direction  perpendicular  to  the  surface,  should, 
accordingly,  move  faster  in  the  denser  body  than  in  the 


280 


INDUCTIVE  LOGIC 


rarer  one  outside.  On  the  other  hand,  according  to  Huy- 
ghens’s  theory,  the  opposite  effect  should  take  place,  — light 
being  refracted  towards  the  vertical  at  the  horizontal  sur- 
face of  a dense  body  such  as  water,  its  velocity  in  the  dense 
body  should  be  less  than  its  velocity  in  the  rare  body.  The 
experiments  separately  made  by  Fizeau  and  Foucault,  both 
gave  the  result  that  in  water  light  moves  slower  than  in 
air,  and  therefore  the  theory  of  Huyghens,  which  was  in 
accord  with  such  a fact,  was  verified,  and  the  theory  of 
Newton,  which  was  radically  out  of  harmony  with  such  a 
fact,  was  discredited.1 

We  cannot  theorize  concerning  nature  to  any  considerable 
extent  without  resorting  to  nature  again  to  correct  aberra- 
tions of  reason,  and  the  false  fancies  of  the  imagination. 
Theory,  if  correctly  formulated,  will  always  lead  to  a 
representation  of  facts  as  they  are ; just  as  facts  as  they 
are,  if  rightly  interpreted,  will  always  lead  to  correct 
theory. 

The  following  are  illustrations  of  the  value  of  this  method 
in  predicting  results  before  unknown. 

“ Halley  had  the  glory  of  having  first  detected  a periodic 
comet  in  the  case  of  that  which  has  since  borne  his  name. 
In  1705,  Halley  explained  how  the  parabolic  orbit  of  a 
planet  may  be  determined  from  three  observations ; and 
joining  example  to  precept,  himself  calculated  the  positions 
and  orbits  of  twenty-four  comets.  He  found,  as  the  reward 
of  his  industry,  that  the  comets  of  1607  and  1531  had  the 
same  orbit  as  that  of  1682.  And  here  the  intervals  are 
nearly  the  same,  namely,  about  seventy-five  years.  Are 
these  three  comets  then  identical  ? In  looking  back  into 
the  history  of  such  appearances,  he  found  comets  recorded 
in  1456,  in  1380,  and  1305;  the  intervals  are  still  the  same, 
— seventy-five  or  seventy-six  years.  It  was  impossible  now 
to  doubt  that  they  were  the  periods  of  a revolving  body,  its 
orbit  a long  ellipse,  not  a parabola.  If  this  were  so,  the 
1 Tait,  Recent  Advances  in  Physical  Science,  pp.  65,  66. 


PREDICTION  AND  VERIFICATION 


281 


comet  must  reappear  in  1758  or  1759.  Halley  began  his 
laborious  calculations  and  predicted  that  the  comet  would 
reach  its  perihelion  April  13,  1759,  but  claimed  the  license 
of  a month  for  the  inevitable  inaccuracies  of  a calculation  in 
which,  in  addition  to  all  other  sources  of  error,  was  made 
in  haste,  that  it  might  appear  as  a prediction.  The  comet 
justified  his  calculations  and  his  caution  together  ; for  it 
arrived  at  its  perihelion  on  March  13,  1759.”  1 

Another  illustration  of  a like  nature  is  the  prediction  of 
Faraday,  based  upon  Wheatstone’s  experimental  proof  that 
the  conduction  of  electricity  required  time;  namely,  “that 
if  the  conducting  wires  were  connected  with  the  coatings  of 
a large  Leyden  jar,  the  rapidity  of  conduction  would  be 
necessarily  lessened.  This  prediction  was  made  in  1838 
and  was  not  verified  until,  sixteen  years  later,  a submarine 
cable  was  laid  beneath  the  English  Channel.  A considerable 
retardation  of  the  electric  spark  was  then  detected  by 
Siemens  and  Latimer  Clark.  Faraday  at  once  pointed  out 
that  the  wire  surrounded  by  water  resembles  a Leyden  jar 
on  a large  scale:  so  that  each  message  sent  through  the 
cable  verified  his  remark  of  1838.” 2 

In  Pasteur’s  experiments  with  silkworms  already  referred 
to,  he  made  a prediction  in  1866,  when,  having  inspected 
fourteen  parcels  of  eggs  intended  for  incubation,  and  having 
examined  the  moths  which  produced  these  eggs,  he  wrote 
out  the  prediction  of  what  would  occur  in  1867,  and  placed 
the  prophecy  as  a sealed  letter  in  the  hands  of  the  mayor 
of  St.  Hippolyte.  In  1867,  the  cultivators  communicated  to 
the  mayor  their  results.  The  letter  of  Pasteur  was  then 
opened  and  read,  and  it  was  found  that  in  twelve  out  of 
fourteen  cases  there  was  absolute  conformity  between  his 
prediction  and  the  observed  facts.  Many  of  the  groups  had 
perished  totally  ; the  others  had  perished  almost  totally ; 
and  such  was  Pasteur’s  prediction.  In  two  out  of  the 

1 Whewell,  History  of  Inductive  Science,  3d  ed.,  Vol.  II,  p.  182. 

2 Jevons,  Principles  of  Science,  p.  543. 


282 


INDUCTIVE  LOGIC 


fourteen  cases,  instead  of  the  prophesied  destruction,  half 
an  average  crop  was  obtained.1 

Another  interesting  illustration  concerns  Darwin’s  specula- 
tions regarding  the  formation  of  coral  reefs  and  atolls. 
Before  Darwin  wrote  on  the  subject,  it  was  generally  be- 
lieved that  the  coral  atolls  were  formed  by  the  coral  polypes 
growing  upon  submerged  volcanic  craters.  Darwin  insisted 
that  as  the  polypes  cannot  live  below  a depth  of  100  feet, 
and  are  killed  by  exposure  to  sunshine  and  air,  and  could  not 
therefore  have  grown  upward  from  the  vast  depths  to  which 
the  coral  masses  extend,  each  atoll  must  have  begun  as  a 
fringing-reef  about  an  island  almost  touching  the  shore,  and 
with  only  a narrow  and  shallow  channel  of  water  between ; 
and  then  became  a barrier  reef,  that  is,  one  with  a wider 
and  deeper  channel  of  water  separating  from  the  shore, 
owing  to  the  slow  but  progressive  subsidence  of  the  island 
round  which  the  polypes  first  began  to  build.  Then  with 
the  further  and  complete  subsidence  of  the  island  beneath 
the  water,  there  remained  a ring  of  coral  with  a central 
lagoon  forming  the  so-called  atoll.  Darwin  says  in  his 
Autobiography  that  the  main  features  of  his  theory  were 
conceived  while  on  the  voyage,  and  that  even  previous  to 
seeing  a true  coral  reef.2  He  says : “ No  other  work  of 
mine  was  begun  in  so  deductive  a spirit  as  this,  for  the 
whole  theory  was  thought  out  on  the  west  coast  of  South 
America,  before  I had  seen  a true  coral  reef.  I had  only  to 
verify  and  extend  my  views  by  a careful  examination  of 
living  reefs.  But  it  should  be  observed  that  I had  during 
the  two  previous  years  been  incessantly  attending  to  the 
effects  on  the  shores  of  South  America  of  the  intermittent 
elevation  of  the  land,  together  with  denudation  and  deposi- 
tion of  sediment.  This  necessarily  led  me  to  reflect  much 
on  the  effects  of  subsidence,  and  it  was  easy  to  replace  in 
imagination  the  continued  deposition  of  sediment  by  the 

1 Tyndall,  Fragments  of  Science,  pp.  291,  292. 

2 Life  and  Letters  of  Charles  Darwin,  1887,  Vol.  I,  p.  58. 


PREDICTION  AND  VERIFICATION 


283 


upward  growth  of  corals.  To  do  this  was  to  form  my 
theory  of  the  formation  of  barrier  reefs  and  atolls.” 

It  will  thus  be  seen  that  Darwin’s  deduction  was  based 
upon  previous  inductions  in  other  spheres,  the  result  of  his 
own  observation ; he  also  tells  us  in  the  same  connection, 
that  he  had,  in  the  preparation  of  his  work  on  Coral  Reefs, 
spent  twenty  months  of  hard  labor,  reading  every  work  on 
the  island  of  the  Pacific  and  consulting  many  charts.  He 
thus  made  the  widely  extended  observations  of  other  men 
tributary  to  his  inferences  concerning  coral-reef  formations. 
Dr.  Williams  says  of  Darwin’s  insight  in  this  particular : 
“He  saw  more  clearly  than  his  precursors  had  done  the 
validity  of  the  dictum  of  Johannes  Muller  in  this,  and 
indeed  all  his  works,  that  the  most  important  truths  in 
natural  science  are  to  be  discovered,  neither  by  the  mere 
analysis  of  philosophical  ideas,  nor  by  simple  experience, 
but  by  reflective  experience,  which  distinguishes  the  essential 
from  the  accidental  in  the  phenomena  observed,  and  thus 
finds  principles  from  which  many  experiences  can  be 
derived.”  1 This  is  a very  satisfactory  and  striking  account 
of  what  may  be  styled  the  combined  inducto-deductive 
temper  of  mind,  and  especially  as  embodied  in  so  eminent 
a student  of  nature  as  Darwin. 

Bacon  insists  that  anticipations  of  nature  are  sources 
of  innumerable  errors,  and  that  the  truly  scientific  method 
consists  in  an  interpretation  of  nature  as  it  is  revealed  to 
the  perception  through  direct  observation  and  experiment. 
It  is,  however,  largely  through  these  “ anticipations  ” that 
progress  in  science  is  attained.  There  may  be  anticipations 
which  are  considered  final,  and  all  attempts  at  verification 
regarded  as  unnecessary  and  even  as  impertinent.  Results 
deductively  attained  are  then  asserted  with  dogmatic  insist- 
ence, as  though  possessing  the  convincing  power  of  facts 
themselves;  and  all  appeal  to  controverting  or  exceptional 
cases  are  set  aside,  without  even  so  much  as  a respectful 
1 Darwin,  Coral  Reefs.  Prefatory  note  by  Dr.  J.  W.  Williams,  p.  ix. 


284 


INDUCTIVE  LOGIC 


hearing.  Such  anticipations  of  nature  rightfully  fall  under 
the  scornful  reprehension  of  a Bacon.  But  there  are  other 
anticipations  which  serve  as  a spur  to  a more  penetrating 
observation,  and  more  painstaking  experiment,  in  order  to 
square  theory  to  facts.  Such  anticipations  are  the  glory  of 
science ! 

Suppose  such  anticipations  are  disproved  by  subsequent 
experiment  or  observation ; they  have  served  a high  pur- 
pose in  suggesting  investigation  along  lines  which  otherwise 
would  have  remained  unthouglit  of.  Anticipations  alone 
are  barren;  anticipations  leading  to  verification  are  produc- 
tive of  valuable  results.  To  this  the  history  of  scientific 
thought  bears  abundant  testimony.  Professor  Clifford  has 
made  the  power  of  prediction  one  of  the  essential  character- 
istics of  scientific  thought.  He  says,  in  his  essay  on  the 
Aims  and  Instruments  of  Scientific  Thought,  that  “ the  differ- 
ence between  scientific  and  merely  technical  thought  is  just 
this : Both  of  them  make  use  of  experience  to  direct  human 
action  ; but  while  technical  thought  or  skill  enables  a man  to 
deal  with  the  same  circumstances  that  he  has  met  with 
before,  scientific  thought  enables  him  to  deal  with  different 
circumstances  that  he  has  never  met  with  before.” 1 He 
cites  two  illustrations,  which  are  admirable  examples  of 
scientific  prediction.  The  first  relates  to  the  suggestion  of 
Fleeming  Jenkin,  regarding  structural  bracing.  It  had  been 
known  before  that  in  an  arch  every  part  is  compressed  or 
pushed  by  other  parts ; and  every  part  of  a chain  is  in  a 
state  of  tension,  that  is,  pulled  by  the  other  parts.  In  many 
cases  these  forms  are  united  in  the  common  girder,  which 
consists  of  two  main  pieces,  of  which  the  upper  acts  as  an 
arch,  and  is  compressed,  while  the  lower  one  acts  as  a chain 
and  is  pulled.  “Now,”  says  Professor  Clifford,  “suppose 
that  any  good,  practical  engineer  makes  a bridge  or  a roof 
upon  some  approved  pattern  which  has  been  made  before. 
He  designs  the  size  and.  shape  of  it  to  suit  the  opening 
1 Clifford,  Lectures  and  Essays,  Vol.  I,  p.  128. 


PREDICTION  AND  VERIFICATION 


285 


which  has  to  be  spanned ; selects  his  material  according  to 
the  locality ; assigns  the  strength  which  must  be  given  to 
the  several  parts  of  the  structure,  according  to  the  load 
which  it  will  have  to  bear.  There  is  a great  deal  of  thought 
in  the  making  of  this  design,  whose  success  is  predicted  by 
the  application  of  previous  experience ; it  requires  techni- 
cal skill  of  a very  high  order,  but  it  is  not  scientific  thought. 
On  the  other  hand,  Mr.  Fleeming  Jenkin  designs  a roof  con- 
sisting of  two  arches  braced  together,  instead  of  an  arch 
and  a chain  braced  together;  and,  although  this  form  is 
quite  different  from  any  known  structure,  yet  before  it  is 
built  he  assigns  with  accuracy  the  amount  of  material  that 
must  be  put  into  every  part  of  the  structure  in  order  to  bear 
the  required  load,  and  this  prediction  may  be  trusted  with 
perfect  security.  What  is  the  natural  comment  on  this  ? 
Why,  that  Mr.  Fleeming  Jenkin  is  a scientific  engineer.”1 
The  second  illustration  which  Professor  Clifford  gives  is 
as  follows:  “You  know  that  if  you  make  a dot  on  a piece 
of  paper,  and  then  hold  a piece  of  Iceland  spar  over  it,  you 
will  see  not  one  dot,  but  two.  A mineralogist,  by  measur- 
ing the  angles  of  a crystal,  can  tell  you  whether  or  no  it 
possesses  this  property  without  looking  through  it.  He  re- 
quires no  scientific  thought  to  do  that.  But  Sir  William 
Rowan  Hamilton,  the  late  astronomer  royal  of  Ireland, 
knowing  these  facts,  and  also  the  explanation  of  them, 
which  Fresnel  had  given,  thought  about  the  subject,  and 
he  predicted  that  by  looking  through  certain  crystals  in  a 
particular  direction  we  should  see  not  two  dots,  but  a con- 
tinuous circle  of  dots.  Mr.  Lloyd  made  the  experiment  and 
saw  the  circle,  a result  which  had  never  been  even  suspected. 
This  has  always  been  considered  one  of  the  most  signal 
instances  of  scientific  thought  in  the  domain  of  physics.  It 
is  most  distinctly  an  application  of  experience  gained  under 
certain  circumstances  to  entirely  different  circumstances.” 2 

1 Clifford,  Lectures  and  Essays,  Vol.  I,  pp.  127,  128. 

* Ibid.,  Vol.  I,  pp,  128,  129. 


286 


INDUCTIVE  LOGIC 


There  is  also  an  indirect  method  of  prediction,  varying 
somewhat  from  the  one  already  described  and  yet  similar  to 
it.  It  is  called  prediction  by  inversion  of  cause  and  effect. 
There  are  many  cases  in  which  cause  and  effect  are  related 
in  a reciprocal  manner,  so  that  not  only  will  the  cause  pro- 
duce the  effect,  but  the  effect,  operating  as  a cause,  will 
bring  about  the  original  cause  as  an  effect,  it  may  be  in  a 
modified  form  but  clearly  recognizable  as  such.  Professor 
Tyndall  said  of  Faraday  that  “ the  strong  tendency  of  his 
mind  to  look  upon  the  reciprocal  actions  of  natural  forces 
gave  birth  to  his  greatest  discoveries.”1  For  instance,  Oer- 
sted had  proved  that  an  electric  current  will  produce  mag- 
netism, and  Faraday,  taking  this  as  a suggestion,  inferred 
that  magnetism  might  produce  an  electric  current;  in  the 
year  1831  he  devised  a suitable  experiment  of  introducing  a 
bar-magnet  into  a coil  of  insulated  copper  wire,  and  then 
withdrawing  the  magnet  whilst  the  two  ends  of  the  wire 
were  connected  with  a distant  galvanometer,  which  indicated 
the  presence  of  the  electric  current.  Thus,  his  inference 
received  substantial  verification.2 

It  has,  moreover,  been  found  that  when  a given  cause  pro- 
duces a certain  effect,  then  if  the  effect  be  produced  in  some 
other  manner,  the  process  will  tend  to  produce  the  original 
cause,  but  inverted  as  regards  its  direction  or  nature.  For 
instance,  it  is  known  that  heat  will  expand  gases ; now,  if  a 
gas  be  relieved  of  the  pressure  of  the  vessel  enclosing  it,  it 
will  expand  by  virtue  of  its  own  elastic  power,  producing, 
however,  cold  in  the  surrounding  atmosphere.  So  also  heat 
will  cause  a bar  of  iron  to  expand.  Dr.  Joule  proved  that 
if  iron  were  expanded  by  mechanical  force,  it  would  be  ac- 
companied by  cold.  Inasmuch  as  india-rubber  is  related  to 
heat  in  an  opposite  manner  to  that  of  iron,  being  contracted 
by  heat  instead  of  expanded,  we  would,  according  to  the 
law  above  expressed,  naturally  expect  that  a mechanical  ex- 

1 Tyndall,  Fragments  of  Science,  p.  338. 

2 Gore,  The  Art  of  Scientific  Discovery,  p.  594. 


PREDICTION  AND  VERIFICATION 


287 


pansion  of  india-rubber  would  give  beat,  and  a contraction 
produce  cold.  An  experiment  may  be  tried  by  suddenly 
stretching  a rubber  band  while  the  middle  part  is  in  the 
mouth ; when  stretched,  it  grows  warm  ; when  relaxed,  it 
seems  cold.1 

Again,  as  heat  will  melt  many  substances,  if  we  can  re- 
duce the  same  substance  from  the  solid  to  the  liquid  state, 
we  would  expect,  as  a result,  the  opposite  of  heat,  namely, 
cold.  This  occurs  in  all  freezing  mixtures  ; as  the  affinity  of 
salt  for  water  causes  it  to  melt  ice,  thus  producing  cold  in  the 
surrounding  atmosphere,  sufficient  to  freeze  cream  or  other 
similar  substance,  inasmuch  as,  passing  from  solid  to  liquid, 
water  absorbs  heat  from  all  substances  near  it ; this  absorp- 
tion producing  artificial  cold  surrounding  it.  The  recipro- 
cal action  of  heat  and  cold  is  illustrated  in  an  interesting 
experiment  described  by  Tait.2  He  took  a bar  of  ice,  sup- 
ported horizontally  at  either  end,  and  over  the  middle  of 
the  bar  he  put  a fine  wire,  and  put  equal  weights  to  the  two 
ends  of  the  wire.  The  wire  gradually,  by  the  action  of  the 
weights,  cut  through  the  bar  of  ice,  and  yet  it  was  observed 
that  the  path  of  the  wire  was  instantly  replaced  by  the 
freezing  again  of  the  melted  portion  produced  by  the  press- 
ure, and  when  the  wire  had  wholly  traversed  the  entire 
thickness  of  the  bar,  the  bar  itself  was  intact,  and  even 
stronger  along  the  line  of  the  cutting  than  before.  The 
explanation  of  this  experiment  is  that  inasmuch  as  heat 
melts  ice,  then  when  ice  is  melted  by  pressure,  as  in  this 
case  of  the  weighted  wire,  cold,  the  opposite  of  heat,  is  in- 
duced ; thus,  as  the  wire  was  forced  by  the  weights  into  the 
ice,  the  pressure  upon  the  ice  melted  it,  making  it  colder,  so 
that  the  water  produced,  passing  around  the  chilled  wire, 
and  being  thus  relieved  of  pressure,  froze  again. 

Faraday  predicted  certain  magnetic  phenomena  by  this 
method,  which  are  specially  interesting  as  illustrations  of 

1 Jevons,  Principles  of  Science,  p.  545. 

2 Tait,  Recent  Advances  in  Physical  Science,  pp.  99, 100. 


288 


INDUCTIVE  LOGIC 


this  kind  of  prediction.  It  seems  that  Arago  had  observed 
in  1824  that  the  number  of  oscillations  which  a magnetized 
needle  makes  in  a given  time,  under  the  influence  of  the 
earth’s  magnetism,  is  very  much  lessened  by  the  proximity 
of  certain  metallic  masses,  and  especially  of  copper.  Em- 
ploying the  latter  substance  in  an  experiment  upon  a mag- 
netized needle,  he  succeeded  in  reducing  the  number  of  its 
vibrations  in  a given  time  from  three  hundred  to  four.  Tak- 
ing the  experiment  as  a basis  for  his  inference,  Faraday 
predicted  that  since  the  presence  of  a metal  at  rest  stops  the 
oscillations  of  a magnetic  needle,  the  neighborhood  of  a 
magnet  at  rest  ought  to  stop  the  motion  of  a rotating  mass 
of  metal.  He  therefore  proceeded  to  put  his  inference  to 
the  test  of  actual  experiment,  by  suspending  a cube  of  cop- 
per to  a twisted  thread  which  was  placed  between  the  poles 
of  a powerful  electromagnet.  When  the  thread  was  left 
to  itself,  it  began  to  spin  round  with  great  velocity,  but 
stopped  the  moment  a powerful  current  passed  through  the 
electromagnet.1  Again,  as  heat  applied  to  the  junction  of 
two  metallic  bars,  as  antimony  and  bismuth,  produced  an 
electric  current,  it  was  inferred  that  if  an  electric  current 
was  made  to  pass  through  such  a junction,  it  would  pro- 
duce cold,  and  such  proved  to  be  the  case.2 

In  the  general  process  of  verification,  it  often  happens 
that  seeming  exceptions  occur  which  are  direct  contradic- 
tions of  the  law  we  are  attempting  to  prove.  And  it  is  in 
dealing  with  such  cases  that  one’s  power  of  discrimination 
is  most  fully  taxed.  It  is  necessary  to  make  a most  careful 
distinction  between  seeming  and  real  exceptions.  Professor 
Jevons  has  given  a very  exhaustive  classification  of  the  dif- 
ferent kinds  of  exceptional  phenomena,  which  it  is  well  to 
have  in  mind,  in  order  to  know  in  any  investigation  the 
various  possible  complications  that  may  rise.3  The  excep- 
tional phenomena,  as  given  by  Jevons,  are  : — 

1 Ganot,  Physics,  pp.  797,  798.  2 Jevons,  Principles  of  Science,  p.  547. 

8 See  Jevons,  Chapter  XXIX,  in  his  Principles  of  Science , on  “ Excep- 
tional Phenomena.” 


PREDICTION  AND  VERIFICATION 


289 


1.  Imaginary,  or  false  exceptions  ; that  is,  facts,  objects, 
or  events  which  are  not  really  what  they  are  supposed  to 
be. 

2.  Apparent  but  congruent  exceptions,  which,  though  ap- 
parently in  conflict  with  a law  of  nature,  are  really  in  agree- 
ment with  it. 

3.  Singular  exceptions,  which  really  agree  with  a law  of 
nature,  but  exhibit  remarkable  and  unique  results  of  it. 

4.  Divergent  exceptions,  which  really  proceed  from  the 
ordinary  action  of  known  processes  of  nature,  but  which  are 
excessive  in  amount  or  monstrous  in  character. 

5.  Accidental  exceptions,  arising  from  the  interference 
of  some  entirely  distinct  but  known  law  of  nature. 

6.  Novel  and  unexplained  exceptions,  which  lead  to  the 
discovery  of  a new  series  of  laws  and  phenomena,  modifying 
or  disguising  the  effects  of  previously  known  laws  without 
being  inconsistent  with  them. 

7.  Limiting  exceptions,  showing  the  falsity  of  a supposed 
law  to  some  cases  to  which  it  had  been  extended,  but  not 
affecting  its  truth  in  other  cases. 

8.  Contradictory,  or  real,  exceptions,  which  lead  us  to  the 
conclusion  that  a supposed  hypothesis  or  theory  is  in  oppo- 
sition to  the  phenomena  of  nature,  and  must  therefore  be 
abandoned. 

It  will  be  seen  that  among  so  many  possibilities  of  inter- 
pretation an  exception  does  not  necessarily  prove  the  rule, 
as  the  old  adage  would  have  it ; nor  does  the  exception,  on 
the  other  hand,  necessarily  disprove  the  rule  or  law.  It 
must  be  in  each  case  strictly  and  adequately  interpreted, 
which  requires  a penetrating  sagacity  and  a thorough 
knowledge  of  the  phenomena  under  investigation. 

In  the  process  of  verification,  the  question  naturally  sug- 
gests itself : How  many  verifying  instances  are  sufficient  to 
determine  the  universal  validity  of  a given  law  ? This  ques- 
tion will  be  recognized  as  an  old  difficulty,  now  presented 
in  another  form ; but  in  reality  it  is  the  perplexing  problem 


290 


INDUCTIVE  LOGIC 


of  determining  tire  logical  ground  of  induction.  What  is  our 
warrant  for  proceeding  from  known  and  verified  instances 
to  unknown  phenomena,  of  the  same  kind  it  is  true,  but  as 
yet  beyond  the  pale  of  our  experience  ? The  warrant  for 
our  generalization  does  not  lie  wholly  in  the  number  of  veri- 
fying instances.  In  addition  to  the  effect  which  mere  num- 
ber produces  in  confirming  our  belief,  there  is  the  confidence 
which  we  feel  in  the  constancy  of  the  order  of  nature,  and 
which  we  are  constrained  to  assume  as  a fundamental  postu- 
late.1 Therefore,  we  say  that  the  verifying  facts  must  be 
of  such  a number,  and  of  such  a nature  as  well,  that  they 
give  evidence  of  a uniformity  which  transcends  all  supposi- 
tion of  mere  coincidence,  and  compels  us  to  attribute  it  to 
the  uniformity  of  nature  itself,  in  which  we  find  a warrant 
for  our  generalization.  As  Professor  Clifford  has  remarked  : 
“ The  aim  of  scientific  thought  is  to  apply  past  experiences 
to  new  circumstances.  The  instrument  is  an  observed  uni- 
formity in  the  course  of  events.  By  the  use  of  this  instru- 
ment it  gives  us  information  transcending  our  experience, 
it  enables  us  to  infer  things  that  we  have  not  seen  from 
things  that  we  have  seen  ; and  the  evidence  for  the  truth 
of  that  information  depends  on  our  supposing  that  the  uni- 
formity holds  good  beyond  our  experience.” 2 

In  extending  knowledge  and  predicting  results  beyond 
the  sphere  of  experience,  modern  scientific  investigation  is 
largely  indebted  to  the  principles  and  methods  of  mathe- 
matics. Mathematical  laws,  applied  to  the  data  given  in 
sense-perception,  give  indications  of  the  necessary  relations 
that  must  exist  in  the  observed  phenomena,  and  all  that 
they  involve.  Thus,  that  which  is  given  directly  in  con- 
sciousness is  supplemented  by  that  which  is  given  indirectly 
as  mathematically  necessitated.  The  mathematico-experi- 
mental  method  in  physics  has  led  to  very  rich  and  impor- 
tant results  which  have  proved  practically  its  efficiency  as 
a scientific  method. 

1 See  Sigwart,  Logic,  Vol.  II,  p.  348. 

2 Clifford,  Lectures  and  Essays,  Vol.  I,  pp.  131,  132. 


CHAPTER  XII 


HYPOTHESIS 

The  inductive  process  cannot  proceed  to  any  great  extent 
or  attain  satisfactory  results  without  the  aid  of  some  hy- 
pothesis. An  hypothesis  is  a supposition  regarding  the 
cause  of  a phenomenon,  which  we  make  either  as  prelimi- 
nary to  an  experiment  which  will  prove  or  disprove  the 
supposition,  or  in  lieu  of  an  experiment  or  systematic  obser- 
vation, when  such  are  impossible  owing  to  the  peculiar 
conditions  of  the  phenomenon  itself.  We  see  therefore 
that  the  framing  of  hypotheses  has  a double  function.  First, 
considered,  as  preliminary  to  experiment,  — we  found  that 
in  cases  where  two,  three,  or  more  elements  enter  into 
a complex  antecedent,  it  is  impossible  often,  and  always 
impracticable  to  test  the  various  possible  combinations  sepa- 
rately in  order  to  note  their  different  results.  The  com- 
binations in  complex  phenomena  are  indefinitely  great, 
and  the  isolation  of  certain  elements  in  order  to  estimate 
the  exact  result  of  the  combined  force  of  the  other  combina- 
tions is  extremely  difficult  and  often  impossible.  Therefore 
the  mind  discards  some  combinations  as  irrelevant,  others 
as  impossible,  and  selects  one  perhaps  as  the  most  likely 
cause  of  the  given  effect.  This  selective  function  of  the 
mind,  therefore,  indicates  the  line  of  experiment  in  a de- 
terminate manner  and  does  not  leave  the  phenomena  to 
indeterminate  and  haphazard  investigation. 

Consider,  for  instance,  so  eminent  an  experimenter  as 
Charles  Darwin,  so  fertile  in  all  kinds  of  experimental  re- 
sources ; yet  it  is  said  of  him  that  every  experiment  was  the 
result  of  a tentative  theory,  thought  out  in  advance  of  all 

291 


292 


INDUCTIVE  LOGIC 


actual  test  and  by  a sagacious  insight  into  the  necessary 
conditions  of  the  interrelated  phenomena  before  him.  His 
son,  Francis  Darwin,  says  of  him  in  his  Reminiscences  : 
“He  often  said  that  no  one  could  be  a good  observer  un- 
less he  was  an  active  theorizer.  It  was  as  though  he  were 
charged  with  theorizing  power  ready  to  flow  into  any 
channel  on  the  slightest  disturbance,  so  that  no  fact,  how- 
ever small,  could  avoid  releasing  a stream  of  theory,  and 
thus  the  fact  became  magnified  into  importance.  In  this 
way,  it  naturally  happened  that  many  untenable  theories 
occurred  to  him ; but  fortunately  his  richness  of  imagina- 
tion was  equalled  by  his  power  of  judging  and  condemning 
the  thoughts  that  occurred  to  him.  He  was  just  to  his 
theories,  and  did  not  condemn  them  unheard ; and  so  it 
happened  that  he  was  willing  to  test  what  would  seem  to 
most  people  not  at  all  worth  testing.  These  rather  wild 
trials  he  called  ‘ fool’s  experiments,’  and  enjoyed  extremely. 
As  an  example,  I may  mention  that,  finding  the  cotyledons 
of  Biophytum  to  be  highly  sensitive  to  vibrations  of  the  table, 
he  fancied  that  he  might  perceive  the  vibrations  of  sound, 
and  therefore  made  me  play  my  bassoon  close  to  a plant.  The 
love  of  experiment  was  very  strong  in  him,  and  I can  remem- 
ber the  way  he  would  say,  ‘ I shan’t  be  easy  till  I have  tried 
it,’  as  if  an  outside  force  were  driving  him.”1  Hypothesis 
and  experiment  were  in  the  hand  of  Darwin  like  a two- 
edged  sword,  which  he  employed  with  rare  skill  and  effect. 

An  hypothesis  is  to  be  regarded  not  only  as  the  precursor 
of  experiment,  but  it  also  functions  as  a method  of  explana- 
tion when  actual  verification  is  impossible.  We  see  this 
constantly  in  our  everyday  life.  We  are  compelled  again 
and  again  to  account  for  situations  which  occur  that  are 
impossible  for  us  to  reproduce  in  the  form  of  an  experi- 
ment, that  we  are  able  to  observe  but  once.  Some  explana- 
tion is  required  to  satisfy  mental  demands  which  are 
imperative  in  this  regard.  The  explanation  which  seems 
1 Life  and  Letters  of  Charles  Darwin,  Vol.  I,  p.  126. 


HYPOTHESIS 


293 


most  in  keeping  with  the  sum  of  facts  in  our  possession, 
is  the  hypothesis  which  we  frame ; so  also  in  explaining 
the  conduct  of  others  by  conjecture  as  to  the  most  reason- 
able motives  that  will  satisfactorily  account  for  the  same ; 
such  hypotheses  we  are  constantly  compelled  to  assume. 
We  are  not  always  able  to  perceive  the  relations  existing 
between  facts  as  they  come  into  the  sphere  of  our  experience, 
and  yet  we  are  constrained  to  think  of  them  as  related ; but 
in  order  to  systematize  them,  we  must  supply  mentally  the 
lacunae  which  appear  in  the  phenomena  as  perceived.  This 
supposition  that  is  necessary  to  construct  facts  into  a system 
is  an  hypothesis. 

An  illustration  of  an  hypothesis  suggesting  systematic 
observation  and  experiment  is.  found  in  the  history  of  the 
discovery  of  vaccination  by  Jenner.  It  seems  that  while  a 
mere  youth,  pursuing  his  studies  at  Sodbury,  he  chanced  to 
hear  a casual  remark  made  by  a country  girl  who  came  to 
his  master’s  shop  for  advice.  The  smallpox  was  mentioned, 
when  the  girl  said,  “I  cannot  take  that  disease,  for  I have 
had  cowpox.”  1 This  observation,  expressing  the  common 
superstition  of  the  simple  country  folk,  appealed  to  Jenner’s 
mind  as  an  inchoate  hypothesis.  Seizing  upon  it  as  a sugges- 
tion of  possible  value,  he  proceeded  to  make  diligent  in- 
quiries and  careful  observations,  which  finally  led  him  to 
the  discovery  of  vaccination. 

An  illustration  of  hypothesis  as  explanation  of  phenomena 
beyond  the  range  of  experiment  is  found  in  the  hypothesis 
as  to  the  source  of  the  sun’s  energy.  An  enumeration  of  the 
different  hypotheses  advanced  upon  this  subject  is  given  by 
Tait  in  his  Recent  Advances  in  Physical  Science ? “ The  old 

notion  that  the  sun  is  a huge  fire,  or  something  of  that  kind, 
is  one  which  will  only  occur  to  one  thinking  of  the  matter 
for  the  first  time ; but  with  our  modern  chemical  knowl- 
edge, we  are  enabled  to  say  that,  massive  as  the  sun  is, 
if  its  materials  had  consisted  of  the  very  best  materials  for 
1 Gore,  The  Art  of  Scientific  Discovery,  p.  495.  1 pp.  151  ff. 


294 


INDUCTIVE  LOGIC 


giving  out  heat,  that  enormous  lhass  of  some  400,000  miles 
in  radius  could  have  supplied  us  with  only  about  5000  years 
of  the  present  radiation.  A mass  of  coal  of  that  size  would 
have  produced  very  much  less  than  that  amount  of  heat. 
Nor  would  the  most  energetic  chemicals  known  to  us',  com- 
bined in  proportion  for  giving  the  greatest  amount  of  heat 
by  actual  chemical  combination,  supply  the  sun’s  present 
waste  for  even  5000  years.  Therefore  as  we  all  know  that 
geological  facts,  if  there  were  no  others,  point  to  at  least  as 
high  a radiation  from  the  sun  as  the  present,  for  at  all 
events  a few  hundreds  of  thousands  of  years  back,  — and 
perhaps  also  indicate  even  a higher  rate  of  radiation  from 
the  sun  in  old  time  than  at  present,  — it  is  quite  obvious 
that  the  heat  of  the  sun  cannot  possibly  be  .supplied  by  any 
chemical  process  of  which  we  have  the  slightest  conception. 

“Now,  if  we  can  find,  oil  the  other  hand,  any  physical 
explanation  of  this  consistent  with  any  present  knowledge, 
we  are  bound  to  take  it  and  use  it  as  far  as  we  can,  rather 
than  say : This  question  is  totally  unanswerable  unless  there 
be  chemical  agencies  at  work  in  the  sun  of  a far  more  power- 
ful order  than  anything  we  meet  with  on  the  earth’s  surface. 
If  we  can  find  a thoroughly  intelligible  source  of  heat,  which, 
though  depending  upon  a different  physical  cause  from  the 
usual  one,  combustion,  is  amply  sufficient  to  have  supplied 
the  sun  with  such  an  amount  of  heat  as  to  enable  it  to 
radiate  for  perhaps  the  last  hundred  millions  of  years  at 
the  same  rate  as  it  is  now  radiating,  then  I say  we  are  bound 
to  try  that  hypothesis  first,  and  argue  upon  it  until  we  find 
it  inconsistent  with  something  known.  And  if  we  do  not 
find  it  inconsistent  with  anything  that  is  known,  while  we 
find  it  completely  capable  of  explaining  our  difficulty,  then 
it  is  not  only  philosophic  to  say  that  it  is  most  probably  the 
origin  of  the  sun’s  energy,  but  we  feel  ourselves  constrained 
to  admit  it.  Newton  long  ago  told  us  this  obligation  in  his 
Rules  of  Philosophizing.  Now  it  is  known  that  if  we  were  to 
take  a mass  of  the  most  perfect  combustibles  which  we  know, 


HYPOTHESIS 


295 


and  let  it  fall  upon  the  sun  merely  from  the  earth’s  distance, 
then  the  work  done  upon  it  by  the  sun’s  attraction  during 
its  fall  would  give  it  so  large  an  amount  of  kinetic  energy 
when  it  reached  the  sun’s  surface  as  to  produce  an  impact 
which  would  represent  six  thousand  times  the  amount  of 
energy  which  could  be  produced  by  its  mere  burning. 

“ It  appears,  then,  that  our  natural  and  only  trustworthy 
mode  of  explaining  the  sun’s  heat  at  present,  in  time  past, 
and  for  time  to  come,  must  be  something  closely  analogous 
to,  but  not  identical  with,  what  was  called  the  nebular 
hypothesis  of  Laplace,  — the  hypothesis  of  the  falling  to- 
gether (from  rudely  scattered  distribution  in  space)  of  the 
matter  which  now  forms  the  various  suns  and  planets.  We 
find  by  calculation  in  which  there  is  no  possibility  of  large 
error,  that  this  hypothesis  is  thoroughly  competent  to  ex- 
plain one  hundred  millions  of  years’  solar  radiation  at  the 
present  rate,  perhaps  more ; and  it  is  capable  of  showing  us 
how  it  is  that  the  sun,  for  thousands  of  years  together,  can 
part  with  energy  at  the  enormous  rate  at  which  it  does  still 
part  with  it,  and  yet  not  apparently  cool  by  perhaps  any 
measurable  quantity. 

“ In  confirmation  of  this,  not  only  is  the  hypothesis  itself 
capable  of  explaining  the  amounts  of  energy  which  are  in 
question,  but  also  recent  investigations,  aided  by  the  spec- 
troscope, have  shown  us  that  there  are  gigantic  nebular  sys- 
tems at  great  distances  from  our  solar  system,  in  the  process 
of  physical  degradation  in  that  very  way,  by  the  falling  to- 
gether of  scattered  masses,  and  with  numerous  consequent 
developments  of  heat  by  impacts.  What  are  called  tempo- 
rary stars  form  another  splendid  and  still  more  striking 
instance  of  it,  as  where  a star  suddenly  appears,  of  the 
first  magnitude,  or  even  brighter  than  the  first,  outshining 
all  the  planets  for  a month  or  two  at  a time,  and  then, 
after  a little  time,  becomes  invisible  in  the  most  power- 
ful telescope.  Things  of  that  kind  are  constantly  occur- 
ring on  a larger  or  smaller  scale,  and  they  can  all  be  easily 


296 


INDUCTIVE  LOGIC 


explained  on  this  supposition  of  the  impact  of  gravitating 
masses.” 

Such  a hypothesis,  it  will  be  seen,  embraces  all  the  facts 
observed  in  one  self-consistent  system.  The  other  hypotheses 
are  inadequate  to  account  satisfactorily  for  the  phenomena. 
The  validity  of  this  hypothesis  lies  in  its  being  both  ade- 
quate and  congruent  as  well ; experiment  or  corroborative 
observation  being  out  of  the  question,  we  are,  as  Tait  says, 
“ constrained  to  admit  it.” 

Mr.  Darwin  gives  an  enumeration  and  criticism  of  the 
different  hypotheses  which  have  been  suggested  to  explain 
the  extinction  of  the  gigantic  animals  known  to  have  existed 
upon  the  earth.  His  account  will  give  an  indication  of  the 
natural  propensity  of  the  mind  to  frame  hypotheses  con- 
cerning phenomena  which  lie  outside  the  sphere  both  of 
observation  and  experiment.  Mr.  Darwin  says : “ It  is  im- 
possible to  reflect  on  the  changed  state  of  the  American 
Continent  without  the  deepest  astonishment.  Formerly  it 
must  have  swarmed  with  great  monsters  ; now  we  find  mere 
pigmies  compared  with  the  antecedent  allied  races.  The 
greater  number,  if  not  all,  of  these  extinct  quadrupeds, 
lived  at  a late  period,  and  were  the  contemporaries  of  most 
of  the  existing  sea-shells.  What,  then,  has  exterminated  so 
many  species  and  whole  genera  ? The  mind  at  first  is  irre- 
sistibly hurried  into  the  belief  of  some  great  catastrophe ; 
but  thus  to  destroy  animals,  both  large  and  small,  in  South- 
ern Patagonia,  in  Brazil,  on  the  Cordillera  of  Peru,  in  North 
America  up  to  Behring’s  Straits,  we  must  shake  the  entire 
framework  of  the  globe. 

“ An  examination,  moreover,  of  the  geology  of  La  Plata 
and  Patagonia  leads  to  the  belief  that  all  the  features  of  the 
land  result  from  slow  and  gradual  changes.  It  appears  from 
the  character  of  the  fossils  in  Europe,  Asia,  Australia,  and 
in  North  and  South  America,  that  those  conditions  which 
favor  the  life  of  the  larger  quadrupeds  were  lately  coexten- 
sive with  the  world.  What  those  conditions  were,  no  one 


HYPOTHESIS 


297 


has  yet  even  conjectured.  It  could  hardly  have  been  a 
change  of  temperature,  which  at  about  the  same  time  de- 
stroyed the  inhabitants  of  tropical,  temperate,  and  arctic 
latitudes  on  both  sides  of  the  globe.  In  North  America  we 
positively  know  from  Mr.  Lyell  that  the  large  quadrupeds 
lived  subsequently  to  that  period  when  boulders  were 
brought  into  latitudes  at  which  icebergs  now  never  arrive ; 
from  conclusive  but  indirect  reasons  we  may  feel  sure  that  in 
the  southern  hemisphere  the  Macrauchenia  also  lived  long 
subsequently  to  the  ice-transporting  boulder-period.  Did 
man,  after  his  first  inroad  into  South  America,  destroy,  as 
has  been  suggested,  the  unwieldy  Megatherium  and  the  other 
Edentata?  We  must  look  at  least  to  some  other  cause  for 
the  destruction  of  the  little  tucutuco  at  Bahia  Blanca,  and 
of  the  many  fossil  mice  and  other  small  quadrupeds  in 
Brazil.  No  one  will  imagine  that  a drought,  even  far  severer 
than  those  which  cause  such  losses  in  the  provinces  of  La 
Plata,  could  destroy  every  individual  of  every  species  from 
Southern  Patagonia  to  Behring’s  Straits.  What  shall  we 
say  of  the  extinction  of  the  horse  ? Did  those  plains  fail 
of  pasture  which  have  since  been  overrun  by  thousands  and 
hundreds  of  thousands  of  the  descendants  of  the  stock  in- 
troduced by  the  Spaniards  ? Have  the  subsequently  intro- 
duced species  consumed  the  food  of  the  great  antecedent 
races  ? Can  we  believe  that  the  Capybara  has  taken  the 
food  of  the  Toxodon,  the  Guanaco  of  the  Macrauchenia,  the 
existing  small  Edentata  of  their  numerous  gigantic  proto- 
types ? Certainly  no  fact  in  the  long  history  of  the  world 
is  so  startling  as  the  wide  and  repeated  exterminations  of  its 
inhabitants.”1  Mr,  Darwin’s  own  hypothesis  concerning 
this  phenomenon  is  rather  indefinite,  but  nevertheless  as 
definite  as  the  extreme  complexity  of  the  facts  will  allow. 
He  says  that  there  are  certain  causes  operating  in  nature, 
their  exact  character  remaining  unknown,  such  that  the  too 
rapid  increase  of  every  species,  even  the  most  favored,  is 
1 Darwin,  Voyage  of  a Naturalist,  Yol.  I,  p.  223. 


298 


INDUCTIVE  LOGIC 


steadily  checked,  producing  in  some  cases  rarity  and  m 
others  extinction,  if  these  causes  operate  with  unusual  effi- 
cacy. His  hypothesis  marks  a tendency  whose  nature, 
nevertheless,  remains  concealed. 

In  all  these  widely  differing  hypotheses  we  see  a certain 
mental  constraint  to  offer  some  explanation,  even  though  it 
be  but  a disguised  confession  of  ignorance,  as  in  Mr.  Darwin’s 
hypothesis. 

An  illustration  of  an  hypothesis  to  explain  observed  phe- 
nomena that  cannot  be  further  tested  is  that  given  in  the 
following  instance  cited  by  Professor  Tyndall : “ At  Erith, 
in  1804,  there  occurred  a tremendous  explosion  of  a powder 
magazine.  The  village  of  Erith  was  some  miles  distant 
from  the  magazine,  but  in  nearly  all  cases  the  windows 
were  shattered ; and  it  was  noticeable  that  the  windows 
turned  away  from  the  origin  of  the  explosion  suffered 
almost  as  much  as  those  which  faced  it.  Lead  sashes  were 
employed  in  Erith  church  ; and  these,  being  in  some  degree 
flexible,  enabled  the  windows  to  yield  to  pressure  without 
much  fracture  of  glass.  Every  window  in  the  church,  front 
and  back,  was  bent  inwards.  In  fact,  as  the  sound-wave 
reached  the  church,  it  separated  right  and  left,  and,  for  a 
moment,  the  edifice  was  clasped  by  a girdle  of  intensely 
compressed  air,  which  forced  all  its  windows  inwards. 
After  compression,  the  air  in  the  church  no  doubt  dilated, 
and  tended  to  restore  the  windows  to  their  first  condition. 
The  bending  in  of  the  windows,  however,  produced  but  a 
small  condensation  of  the  whole  mass  of  air  within  the 
church ; the  force  of  the  recoil  was,  therefore,  feeble  in  com- 
parison with  the  force  of  impact,  and  insufficient  to  undo 
what  the  latter  had  accomplished.”1  Here  also  is  a set  of 
conditions  that  must  be  satisfied  by  a correct  hypothesis. 
The  phenomenon  was  not  capable  of  repetition  by  any 
experiment.  Professor  Tyndall,  therefore,  pictures  to  his 
mind  what  must  have  happened  beyond  that  which  was 
1 Tyndall,  On  Sound,  p.  23. 


HYPOTHESIS 


299 

observed,  in  order  to  account  for  the  result  which  actually- 
happened.  He  tills  up  the  unseen  from  what  he  knows  of 
the  nature  of  sound-waves,  and  thus  constructs  one  self- 
consistent  system  which  includes  both  the  seen  and  the 
unseen,  the  known  and  the  unknown,  the  observed  and  the 
inferred. 

It  will  be  noticed  in  this  and  other  illustrations  of 
hypothesis,  how  large  a part  is  played  by  the  imagination. 
It  is  the  imagination  which  fills  out  the  vacant  spaces  in 
the  picture  of  perception.  With  some,  the  function  of 
imagination  is  associated  with  fancy  rather  than  fact. 
It  must,  in  this  connection  however,  be  clearly  emphasized 
that  the  imagination  which  constructs  hypotheses  must  be 
throughout  in  touch  with  fact.  It  must  represent  to  the 
mind,  not  what  fancy  suggests,  but  what  the  known  facts 
necessitate.  The  unseen  is  constructed  out  of  the  deter- 
mining conditions  of  the  seen.  It  is  this  deductive  func- 
tion of  the  imagination  that  gives  to  it  a strictly  logical 
significance.  For  instance,  Professor  Tyndall’s  reasoning 
concerning  the  Erith  church  was  somewhat  as  follows:  The 
windows  are  all  bent  inward,  therefore  the  pressure  must  have 
operated  on  all  sides  from  without,  inward ; such  pressure 
could  only  occur  upon  the  supposition  that  the  sound-waves, 
separating  right  and  left,  wholly  encompassed  the  church, 
etc.  In  each  case,  that  which  he  pictured  to  his  mind  as 
happening,  was  regarded  by  him  as  actually  necessitated 
by  the  facts  as  observed. 

Professor  Tyndall  has  most  admirably  discussed  the 
Scientific  Use  of  the  Imagination;  and  his  lecture  under 
that  title  every  student,  both  of  logic  or  of  science,  should 
read.  I quote  one  passage  from  it,  which  has  special  bear- 
ing upon  what  has  just  been  said:  “ We  are  gifted  with  the 
power  of  Imagination,  — - combining  what  the  Germans  call 
Anschauungsgabe  and  Einbildungskraft,  — and  by  this  power 
we  can  lighten  the  darkness  which  surrounds  the  world  of 
the  senses.  There  are  tones  in  science  who  regard  imagina- 


300 


INDUCTIVE  LOGIC 


tion  as  a faculty  to  be  feared  and  avoided  rather  than  em- 
ployed. They  had  observed  its  action  in  weak  vessels  and 
were  unduly  impressed  by  its  disasters.  But  they  might 
with  equal  justice  point  to  exploded  boilers  as  an  argument 
against  the  use  of  steam.  Bounded  and  conditioned  by  co- 
operant Reason,  imagination  becomes  the  mightiest  instru- 
ment of  the  scientific  discoverer.  Newton’s  passage  from 
a falling  apple  to  a falling  moon  was,  at  the  outset,  a leap 
of  the  imagination.  When  William  Thomson  tries  to  place 
the  ultimate  particles  of  matter  between  his  compass  points, 
and  to  apply  to  them  a scale  of  millimetres,  he  is  powerfully 
aided  by  this  faculty.  And  in  much  that  has  been  recently 
said  about  protoplasm  and  life,  we  have  the  outgoings  of 
the  imagination  guided  and  controlled  by  the  known  analo- 
gies of  science.  In  fact,  without  this  power  our  knowledge 
of  nature  would  be  a mere  tabulation  of  coexistences  and 
sequences.  We  should  still  believe  in  the  succession  of  day 
and  night,  of  summer  and  winter;  but  the  soul  of  Force 
would  be  dislodged  from  our  universe;  causal  relations 
would  disappear,  and  with  them  that  science  which  is  now 
binding  the  parts  of  nature  to  an  organic  whole.”1 

In  all  the  illustrations  which  have  been  given,  and,  in 
fact,  in  all  examples  of  the  framing  of  hypotheses,  it  will 
be  seen  that  the  mental  functions  specially  in  operation  are 
those  of  analysis  and  synthesis,  — a separation  of  the  ele- 
ments as  far  as  possible  into  their  simplest  forms  of  expres- 
sion, and  the  building  them  together  into  some  one  system 
whose  unity  lies  in  the  assumed  hypothesis.  Mr.  Venn  has 
especially  emphasized  this  aspect  of  hypothesis,  and  his 
chapter  on  this  subject  will  well  repay  a careful  reading.2 

Every  supposition  however  is  not  necessarily  an  hypoth- 
esis in  the  logical  or  scientific  significance  of  that  term.  It 
will  be  necessary  therefore  to  mention  some  of  the  require- 
ments which  a logical  hypothesis  should  satisfy. 

1 Tyndall,  Use  and  Limit  of  the  Imagination  in  Science,  p.  16. 

2 Venn,  Empirical  Logic,  Chapter  XVI. 


HYPOTHESIS 


301 


1.  An  hypothesis  should  be  plausible ; that  is,  it  should 
be  no  fanciful,  or  merely  conjectural,  explanation  of  the 
phenomena  in  question.  The  suppositions  of  the  interfer- 
ence of  spirits,  or  in  a mythological  age  of  the  gods,  to  ac- 
count for  perplexing  situations  or  obscure  happenings,  have 
no  rank  as  hypotheses;  so,  also,  Fate  is  often  referred  to  as 
a convenient  confession  of  ignorance  in  lieu  of  a satisfactory 
explanation.  Spinoza  has  remarked  upon  this  as  follows : 
“ They  who  have  desired  to  find  scope  for  the  display  of 
their  ingenuity  in  assigning  causes,  have  had  recourse  to  a 
new  style  of  argument  to  help  them  in  their  conclusions, 
namely,  by  reduction,  not  to  the  impossible  or  absurd,  but  to 
ignorance  or  the  unknown,  a procedure  which  shows  very 
plainly  that  there  was  no  other  course  open  to  them.” 

The  difference  between  a scientific  hypothesis  and  a pop- 
ular explanation  concerning  the  same  phenomena  may  be 
found  in  Darwin’s  account  of  “ a strange  belief  which  is  gen- 
eral amongst  the  inhabitants  of  the  Maldiva  atolls,  namely, 
that  corals  have  roots,  and  therefore  that  if  merely  broken 
down  to  the  surface,  they  grow  up  again ; but  if  rooted  out, 
they  are  permanently  destroyed.  By  this  means  the  in- 
habitants keep  their  harbors  clear;  and  thus  the  French 
governor  of  St.  Mary’s  in  Madagascar  ‘cleared  out  and 
made  a beautiful  little  port  at  that  place.’”1  Their  expla- 
nation, however,  is  purely  fanciful,  having  no  basis  in  fact. 
In  contrast,  Darwin’s  hypothesis  to  explain  the  facts  in  the 
case  is  of  a logically  scientific  nature,  and  is  as  follows  : 
Inasmuch  as  loose  sediment  is  injurious  to  the  living  poly- 
pifers,  and  as  it  is  probable  that  sand  would  accumulate  in 
the  hollows  formed  by  tearing  out  the  corals,  but  not  on  the 
broken  and  projecting  stumps,  therefore  in  the  former  case 
the  fresh  growth  of  coral  might  be  thus  prevented  by  the 
deposited  sediment. 

2.  The  second  requirement  is  that  the  hypothesis  must  be 
capable  of  proof  or  disproof.  This  does  not  demand  a test 

1 Darwin,  Coral  Reefs,  p.  89. 


302 


INDUCTIVE  LOGIC 


by  experiment  necessarily ; for  that,  as  we  have  seen,  may 
be  impossible.  It  does,  however,  require  that  some  facts 
should  be  forthcoming  that  will  either  confirm  the  hypoth- 
esis or  disprove  it.  There  are  cases,  however,  as  Lotze  sug- 
gests, whose  very  nature  precludes  the  possibility  of  proving 
or  disproving  the  hypothesis  framed  to  account  .for  them. 
For  instance,  the  very  common  and  simple  hypothesis  of 
regarding  the  stars,  which  are  apparently  but  small  points 
of  light,  as  bodies  of  vast  size,  only  very  remote  from  us, 
is  in  itself  incapable  of  being  either  refuted  or  confirmed 
by  subsequent  discovery.  Lotze  says : “ We  must  abide 
content  if  our  hypotheses  are  thinkable  and  useful,  if  they 
are  capable  of  explaining  all  interconnected  appearances, 
even  such  as  were  still  unknown  when  we  constructed  them, 
if,  that  is  to  say,  they  are  indirectly  confirmed  by  the  agree- 
ment of  all  that  can  be  deduced  from  them  in  thought  with 
the  actual  progress  of  experience.  But  if  we  would  be  so 
fortunate  as  to  find  an  hypothesis  which  will  not  lack  this 
subsequent  confirmation,  we  must  not  simply  assume  any- 
thing that  can  be  barely  conceived  as  real ; we  must  only 
assume  that  which,  besides  being  thinkable,  conforms,  so  to 
speak,  to  the  universal  customs  of  reality,  or  to  the  special 
local  customs  which  prevail  in  that  department  of  phenom- 
ena to  which  the  object  we  are  investigating  belongs.” 1 

It  is  to  be  specially  observed  that  while  the  requirement 
of  proof  of  an  hypothesis  may  be  waived  in  the  sphere 
of  phenomena  where  proof  is  manifestly  impossible,  still, 
where  proof  is  available,  an  hypothesis  must  never  be  so 
framed  as  to  render  the  required  test  either  impossible  or 
impracticable. 

3.  The  hypothesis  must  be  adequate.  It  must  cover  all 
the  facts  in  the  case.  An  outstanding  fact  which  it  cannot 
explain  is  sufficient  to  controvert  such  an  hypothesis.  A 
knowledge  of  the  distinction  between  postulate  and  hypoth- 
esis, and  of  the  relation  which  nominally  exists  between 
1 Lotze,  Logic,  p.  353. 


HYPOTHESIS 


303 


the  two,  will  help  us  to  appreciate  more  clearly  the  force  of 
this  requirement  of  adequacy.  As  defined  by  Lotze,  a pos- 
tulate “expresses  the  conditions  which  must  be  set  up,  or 
the  ground  of  explanation  which  must  be  given  by  some 
reality,  force,  or  event,  before  we  can  think  the  phenomenon 
in  the  form  in  which  it  is  presented  to  us  ; it  thus  requires 
or  postulates  the  presence  of  something  that  can  account 
for  the  given  effect.  An  hypothesis  is  a conjecture  which 
seeks  to  fill  up  the  postulate  thus  abstractly  stated  by  speci- 
fying the  concrete  causes,  forces,  or  processes  out  of  which 
the  phenomenon  really  arose  in  this  particular  case,  while 
in  other  cases  maybe  the  same  postulate  is  to  be  satisfied 
by  utterly  different  though  equivalent  combinations  of  forces 
or  active  elements.”  1 According  to  this  distinction  as  ap- 
plied to  the  problem  of  the  source  of  the  sun’s  energy,  the 
postulate  would  be  the  sum  of  conditions  which  require 
explanation ; namely,  the  tremendous  radiation  of  heat  ex- 
tending through  thousands  and  thousands  of  years.  The 
postulate  therefore  requires  a force  adequate  to  supply  for 
so  long  a period  so  great  an  amount  of  energy.  We  found 
that  ordinary  combustion  of  the  most  highly  combustible 
materials  would  not,  as  an  hypothesis,  satisfy  the  condi- 
tions which  obtain  in  the  postulate ; nor  would  the  libera- 
tion of  chemical  energy  stand  as  an  hypothesis  adequate  to 
satisfy  the  postulate;  the  hypothesis  of  impact  of  masses  upon 
the  sun’s  surface  from  immense  distances  presents  a force 
sufficient  to  meet  the  requirements  of  the  postulate.  More- 
over we  see  in  this  illustration  how  the  hypothesis  is  a par- 
ticular and  concrete  expression  of  the  conditions  expressed 
in  general  and  abstract  terms  in  the  postulate.  The  essential 
characteristic  therefore  of  the  hypothesis  is  that  it  shall 
perfectly  satisfy  all  the  conditions  expressed  in  the  postu- 
late. 

The  hypothesis  that  nature  abhorred  a vacuum,  in  order 
to  account  for  the  rise  of  water  in  a tube  or  pump,  was  seen 
1 Lotze,  Logic,  pp  349,  350. 


304 


INDUCTIVE  LOGIC 


to  break  down  utterly  when  it  was  found  that  the  water  did 
not  rise  beyond  some  thirty-three  feet.  The  demand  of  the 
postulate  in  the  case  was  a force  of  precisely  such  magni- 
tude that  it  would  balance  a column  of  water  thirty-three 
feet  in  height.  This  force,  precisely  satisfying  the  condi- 
tions of  the  postulate,  is  found  in  the  hypothesis  that  the 
atmospheric  pressure  is  such  a magnitude  as  to  exert  a press- 
ure equivalent  to  a column  of  water  some  thirty-three  feet 
in  height.  The  strength  of  the  hypothesis  lies  in  its  exact 
and  appropriate  fitting  into  the  facts  of  the  problem. 

Another  illustration  of  the  fitting  of  hypothesis  to  postu- 
late, and  one  where  the  conditions  of  the  postulate  are  ex- 
tremely complex,  I have  chosen  from  Mr.  Wallace’s  work, 
On  Natural  Selection : “ There  is  a Madagascar  orchis  — 
the  Angrcecum  sesquipedale — with  an  immensely  long  and 
deep  nectary.  How  did  such  an  extraordinary  organ  come 
to  be  developed?  Mr.  Darwin’s  explanation  is  this.  The 
pollen  of  this  flower  can  only  be  removed  by  the  base  of  the 
proboscis  of  some  very  large  moths,  when  trying  to  get  at 
the  nectar  at  the  bottom  of  the  vessel.  The  moths  with  the 
longest  probosces  would  do  this  most  effectually ; they 
would  be  rewarded  for  their  long  tongues  by  getting  the 
most  nectar ; whilst,  on  the  other  hand,  the  flowers  with  the 
deepest  nectaries  would  be  the  best  fertilized  by  the  largest 
moths  preferring  them.  Consequently  the  deepest-nectaried 
orchids  and  the  longest-tongued  moths  would  each  confer  on 
the  other  an  advantage  in  the  battle  of  life.  This  would  tend 
to  their  respective  perpetuation,  and  to  the  constant  length- 
ening of  nectaries  and  probosces.  In  the  Angrcecum  sesqui- 
pedcde  it  is  necessary  that  the  proboscis  should  be  forced 
into  a particular  part  of  the  flower,  and  this  would  only  be 
done  by  a large  moth  burying  its  proboscis  to  the  very  base, 
and  straining  to  drain  the  nectar  from  the  bottom  of  the 
long  tube,  in  which  it  occupies  a depth  of  one  or  two  inches 
only.  Now  let  us  start  from  the  time  when  the  nectary  was 
only  half  its  present  length,  or  about  six  inches,  and  was 


HYPOTHESIS 


305 


chiefly  fertilized  by  a species  of  moth  which  appeared  at 
the  time  of  the  plant’s  flowering,  and  whose  proboscis  was 
of  the  same  length.  Among  the  millions  of  flowers  of  the 
Angroecum  produced  every  year,  some  would  always  be 
shorter  than  the  average,  some  longer.  The  former,  owing 
to  the  structure  of  the  flower,  would  not  get  fertilized,  be- 
cause the  moths  could  get  all  the  nectar  without  forcing 
their  trunks  down  to  the  very  base.  By  this  process  alone 
the  average  length  of  the  nectary  would  annually  increase, 
because  the  short-nectaried  flowers  being  sterile,  and  the 
long  ones  having  abundant  offspring,  exactly  the  same 
effect  would  be  produced  as  if  a gardener  destroyed  the 
short  ones,  and  sowed  the  seed  of  the  long  ones  only;  and 
this  we  know  by  experience  would  produce  a regular  increase 
of  length,  since  it  is  this  very  process  which  has  increased 
the  size  and  changed  the  form  of  our  cultivated  fruits  and 
flowers.  But  this  would  lead  in  time  to  such  an  increased 
length  of  the  nectary  that  many  of  the  moths  could  only 
just  reach  to  the  surface  of  the  nectar,  and  only  the  few 
with  exceptionally  long  trunks  be  able  to  snck  up  a con- 
siderable portion.  This  would  cause  many  moths  to  neglect 
these  flowers,  because  they  could  not  get  a satisfying  sup- 
ply of  nectar,  and  if  these  were  the  only  moths  in  the  coun- 
try, the  flowers  would  undoubtedly  suffer,  and  the  further 
growth  of  the  nectary  be  checked  by  exactly  the  same  pro- 
cess which  had  led  to  its  increase. 

“ But  there  are  an  immense  variety  of  moths,  of  various 
lengths  of  proboscis,  and  as  the  nectary  became  longer, 
other  and  larger  species  would  become  the  fertilizers,  and 
would  carry  on  the  process  till  the  largest  moths  became 
the  sole  agents.  Now,  if  not  before,  the  moth  would  also 
be  affected ; for  those  with  the  longest  probosces  would  get 
the  most  food,  would  be  the  strongest  and  most  vigorous, 
would  visit  and  fertilize  the  greatest  number  of  flowers,  and 
would  leave  the  largest  number  of  descendants.  The  flowers 
most  completely  fertilized  by  these  moths  being  those  which 


306 


INDUCTIVE  LOGIC 


had  the  longest  nectaries,  there  would  in  each  generation 
be,  on  the  average,  an  increase  in  the  length  of  the  nectaries, 
and  also  an  average  increase  in  the  length  of  the  probosces 
of  the  moths ; and  this  would  be  a necessary  result  from  the 
fact  that  nature  ever  fluctuates  about  a mean,  or  that  in 
every  generation  there  would  be  flowers  with  longer  and 
shorter  nectaries,  and  moths  with  longer  and  shorter  pro- 
bosces than  the  average.  I may  here  mention  that  some 
of  the  large  Sphinx  moths  of  the  tropics  have  probosces 
nearly  as  long  as  the  nectary  of  Angrcecum  sesquipedale. 
I have  carefully  measured  the  proboscis  of  a specimen  of 
Macrosila  cluentius  from  South  America,  in  the  collection  of 
the  British  Museum,  and  find  it  to  be  nine  inches  and  a 
quarter  long.  One  from  tropical  Africa  ( Macrosila  morganii ) 
is  seven  inches  and  a half.  A species  having  a proboscis 
two  or  three  inches  longer  could  reach  the  nectar  in  the 
longest  flowers  of  Angrcecum  sesquipedale,  whose  nectaries 
vary  in  length  from  ten  to  fourteen  inches.  That  such  a 
moth  exists  in  Madagascar  may  be  safely  predicted ; 1 and 
naturalists  who  visit  that  island  should  search  for  it 
with  as  much  confidence  as  astronomers  searched  for  the 
planet  Neptune,  — and  I venture  to  predict  they  will  be 
equally  successful.” 2 

I have  given  this  quotation  at  length  in  order  to  indi- 
cate not  only  the  fitting  of  hypothesis  to  the  facts  observed, 
but  also  the  large  and  important  part  performed  by  the 
imagination  in  reproducing  along  parallel  lines  the  natural 
history  of  the  orchid  and  motli.  The  hypothesis  reaches 
back  over  an  indefinitely  long  past,  by  virtue  of  the  neces- 
sities observed  in  the  present,  and  in  accordance  with 
well-established  analogies  and  approved  inductions.  The 
function  of  the  imagination  especially  prominent  is  that  of 

1 It  is  interesting  to  note  that  since  Mr.  Wallace  wrote  the  above,  Kirby, 
in  his  European  Moths  and  Butterflies,  makes  mention'of  one  of  the  Sphin- 
gidx  with  a proboscis  twelve  inches  long! 

2 Wallace,  On,  Natural  Selection,  pp.  271-275. 


HYPOTHESIS 


307 


its  deductive  insight,  which  is  able  to  picture  to  the  mind 
the  inevitable  results  of  this  and  that  condition  as  furnished 
by  the  postulate,  and  then  to  fit  such  necessitated  results 
into  one  self-consistent  system,  with  nothing  left  unex- 
plained, incongruous,  or  contradictory. 

Another  illustration  of  an  hypothesis  covering  a large 
number  of  complex  facts  is  that  of  the  fertilization  of  cer- 
tain flowers  by  means  of  the  wind.  As  given  by  Sir  John 
Lubbock,  we  have  the  following  facts  and  the  correspond- 
ing explanation  of  them:  “ Wind- fertilized  flowers,  as  a 
rule,  have  no  color,  emit  no  scent  and  produce  no  honey, 
and  are  regular  in  form.  Color,  scent,  and  honey  are  the 
three  characteristics  by  which  insects  are  attracted  to 
flowers.  Again,  as  a rule  wind-fertilized  flowers  produce 
much  more  pollen  than  those  which  are  fertilized  by  insects. 
This  is  necessary,  because  it  is  obvious  that  the  chances 
against  any  given  pollen  grain  reaching  the  stigma  are  much 
greater  in  the  one  case  than  in  the  other.  Every  one  has 
observed  the  showers  of  yellow  pollen  produced  by  the 
Scotch  fir.  Again,  it  is  an  advantage  to  wind-fertilized 
plants  to  flower  early  in  the  spring  before  the  leaves  are 
out,  because  the  latter  would  catch  much  of  the  pollen,  and 
thus  interfere  with  its  access  to  the  stigma.  Again,  in  these 
plants  the  pollen  is  less  adherent,  so  that  it  can  be  easily 
blown  away  by  the  wind,  which  would  be  a disadvantage  in 
most  plants  which  are  fertilized  by  insects.  Again,  such 
flowers  generally  have  the  stigma  more  or  less  branched,  or 
hairy,  which  evidently  must  tend  to  increase  their  chances 
of  catching  the  pollen.” 1 There  is  here  a structural  adap- 
tation of  these  plants  to  the  circumstances  designed  to 
explain  them,  so  that  the  consequent  self-consistent  system 
thus  formed  carries  with  it  the  weight  of  conviction. 

There  are  some  explanations  which  do  not  perfectly  cor- 
respond to  reality,  and  yet,  when  their  nature  is  known,  they 
may  be  profitably  used,  not  to  represent  reality,  but  to  assist 
1 Lubbock,  Scientific  Lectures , pp.  9,  10. 


308 


INDUCTIVE  LOGIC 


the  mind  by  an  approximate  representation  to  better  appreci- 
ate the  facts  as  they  really  are  related  one  to  another.  These 
so-called  “ fictions  ” are  useful,  especially  in  mathematics. 
We  suppose,  for  instance,  inscribed  and  circumscribed  poly- 
gons of  a circle,  with  ever-increasing  number  of  sides,  gradu- 
ally approaching  and  becoming  coincident  finally  with  the 
curve  itself.  This  latter  we  know  to  be  impossible,  and  yet 
we  may  treat  that  which  happens  only  approximately  as 
though  really  happening,  merely  as  an  aid  to  the  imagina- 
tion ; and  a fiction,  if  always  so  understood,  may  thus  prove 
helpful  in  the  representation  of  reality  more  clearly  to  our 
minds. 

4.  The  hypothesis  moreover  should  involve  no  contra- 
diction. This  is  clearly  a requirement  that  is  deductive 
rather  than  inductive,  depending  upon  the  fundamental 
principle  of  contradiction  lying  at  the  basis  of  the  deduc- 
tive system  of  logic. 

5.  The  hypothesis  should  be  as  simple  as  possible.  No 
involved  explanation  that  mystifies  rather  than  clears  the 
difficulties  presented  can  rank  as  a true  hypothesis.  Sim- 
plex vert  sigillum.  This  requirement,  of  course,  cannot  in 
all  cases  be  strictly  complied  with ; for  the  phenomena  to 
be  explained  may  present  such  a degree  of  complexity  that 
a simple  hypothesis  would  be  altogether  out  of  the  question. 
For  instance,  the  hypothesis  of  a substance  filling  the  uni- 
verse, and  pervading  all  particles  of  matter,  however  solid 
and  closely  knit  together,  a substance  itself  more  solid  than 
steel,  and  more  elastic  as  well,  such  a supposition  seems  not 
only  too  involved,  but  also  even  to  belie  the  ordinary  judg- 
ments of  common  sense.  And  yet  this  undulatory  hypothe- 
sis is  more  and  more  confirmed  by  every  advance  of  science 
in  the  knowledge  of  the  phenomena  of  light  and  heat. 

It  sometimes  happens  that  the  very  failure  of  am  hy- 
pothesis forms  a substantial  contribution  to  the  progress 
of  thought,  leading  to  the  readjustment  of  a received 
theory,  or  stimulating  research  in  order  to  discover  the 


HYPOTHESIS 


309 


true  in  place  of  the  false  hypothesis.  As  Mr.  Tait  says : 
“We  all  know  that  if  there  had  not  been  a pursuit  after 
the  philosopher’s  stone,  chemistry  could  not  yet  have  been 
anything  like  the  gigantic  science  it  now  is.  In  the  same 
way  we  can  say,  that  modern  physics  could  not  yet  have 
covered  the  ground  it  now  occupies  had  it  not  been  for  this 
experimental  seeking  for  the  so-called  perpetual  motion,  and 
the  consequent  establishment  of  a definite  and  scientifically 
useful  negative.”  1 The  circular  theory  of  the  orbits  of  the 
planets,  while  incorrect,  yet  made  the  transition  easier  from 
the  hypothesis  of  circular  motion  to  that  of  motion  in  an 
elliptical  orbit,  which  is  the  true  theory.  It  often  happens 
that  an  hypothesis  may  not  be  wholly  wrong  but  may  need 
correction,  and  this  is  often  provided  for,  not  by  a total 
rejection  of  the  hypothesis  in  question,  but  by  supplement- 
ing it  by  so-called  subsidiary  hypotheses. 

As  to  the  tests  of  a correct  hypothesis  in  addition  to 
the  fulfilment  of  the  requirements  already  mentioned,  Dr. 
Whewell  has  especially  emphasized  the  importance  of  what 
he  has  styled  a “ Consilience  of  Inductions.”  An  hypothe- 
sis receives  a confirmatory  strengthening  of  its  validity, 
when  it  enables  us  to  explain  and  determine  cases  not 
only  of  the  same  kind  as  the  phenomena  out  of  which  the 
hypothesis  itself  has  developed,  but  cases  which  arise  in  a ' 
sphere  entirely  different  from  that  which  gave  material 
originally  for  the  formation  of  the  hypothesis.  An  hypothe- 
sis that  can  thus  be  carried  into  new  territory  as  an  effec- 
tive instrument  of  research,  is  thereby  doubly  accredited. 
As  Dr.  Whewell  remarks  : “ Accordingly  the  cases  in  which 
inductions  from  classes  of  parts  altogether  different  have 
thus  jumped  together,  belong  only  to  the  best  established 
theories  which  the  history  of  science  contains.  And  as  I 
shall  have  occasion  to  refer  to  this  peculiar  feature  in  their 
evidence,  I will  take  the  liberty  of  describing  it  by  a par- 
ticular phrase  ; and  will  term  it  the  Consilience  of  Inductions. 

1 Tait,  Recent  Advances  in  Physical  Science,  p.  69. 


BIO 


INDUCTIVE  LOGIC 


It  is  exemplified  principally  in  some  of  the  greatest  dis- 
coveries. Thus  it  was  found  by  Newton  that  the  doctrine 
of  the  attraction  of  the  sun  varying  according  to  the  inverse 
square  of  the  distance,  which  explained  Kepler’s  Third  Law, 
of  the  proportionality  of  the  cubes  of  the  distances  to  the 
squares  of  the  periodic  times  of  the  planets,  explained  also 
his  First  and  Second  Laws,  of  the  elliptical  motion  of  each 
planet;  although  no  connection  of  these  laws  had  been  visi- 
ble before.  Again,  it  appeared  that  the  force  of  universal 
gravitation,  which  had  been  inferred  from  the  perturbations 
of  the  moon  and  planets  by  the  sun  and  by  each  other,  also 
accounted  for  the  fact,  apparently  altogether  dissimilar  and 
remote,  of  the  precession  of  the  equinoxes.  Here  was  a most 
striking  and  surprising  coincidence  which  gave  to  the  theory 
a stamp  of  truth  beyond  the  power  of  ingenuity  to  counter- 
feit.” 1 

When  two  rival  hypotheses  can  be  submitted  to  the  test 
of  an  experiment  which  negatives  one  and  confirms  the 
other,  such  a testing  is  called  an  experimentum  crucis.  The 
name  was  first  given  by  Bacon,  and  has  met  with  universal 
acceptance  in  scientific  phraseology.  A crucial  test,  as 
decisive  between  the  emission  and  the  undulatory  theory  of 
light,  is  given  in  an  experiment  first  tried  by  Father  Gri- 
maldi, a Bolognese  monk,  in  1665.  If  a shutter  be  pierced 
with  a very  small  hole,  and  the  luminous  cone  which  passes 
through  the  orifice  be  examined,  the  cone  will  be  found  to 
be  much  less  acute  than  would  be  expected,  considering 
only  the  rectilinear  transmission  of  the  rays,  as  according 
to  the  emission  theory.  If  there  be  interposed  in  the  path 
of  the  luminous  ray  a second  shutter,  pierced  with  a hole 
also,  it  will  be  noticed  that  the  rays  of  the  second  cone  are 
even  more  divergent  than  those  of  the  first.  If  the  image 
of  the  orifice  be  received  upon  a screen,  a white  circle  is 
seen  surrounded  by  a dark  ring,  next  a white  ring,  even 
more  brilliant  than  the  central  portion,  then  a second  dark 
1 Whewell,  Novum  Organum  Renovatum,  Book  II,  Chap.  V,  Art.  110. 


HYPOTHESIS 


311 


ring,  and  finally  another  very  faint  white  ring.  If  in  the 
shutter  with  which  the  experiment  is  made,  two  very  small 
holes  are  pierced  at  a distance  from  each  other  of  one  or 
two  millimetres,  and  the  two  images  received  upon  a screen 
in  such  a manner  that  they  overlap  each  other,  it  is  found 
that  in  the  cuticular  segment  formed  by  the  overlapping  of 
the  images,  the  circles  are  more  obscure  than  in  the  part 
where  they  are  separated.  Thus  by  adding  light  to  light 
darkness  is  produced.1  These  phenomena  are  now  known 
to  be  consistent  only  with  the  undulatory  theory,  and  directly 
in  contradiction  to  the  emission  hypothesis. 

M.  Romanes  performed  several  experiments  upon  bees 
which  had  the  force  of  crucial  tests  of  two  opposed  hypoth- 
eses : one,  that  bees  possess  a general  sense  of  direction, 
irrespective  of  any  special  knowledge  of  their  particular 
surroundings  ; the  other,  that  they  are  guided  in  their  flight 
by  a knowledge  of  the  localities  which  they  have  been  wont 
to  frequent.  M.  Romanes  took  a score  of  bees  in  a box  out 
to  sea,  where  there  could  be  no  landmarks  to  guide  the 
insects  home.  None  of  them  returned  home.  Then  he 
liberated  a second  lot  of  bees  on  the  seashore,  and,  none  of 
these  returning,  he  liberated  another  lot  on  the  lawn  between 
the  shore  and  the  house.  None  of  these  returned,  although 
the  distance  from  the  lawn  to  the  hive  was  not  more  than 
two  hundred  yards.  Lastly,  he  liberated  bees  in  different 
parts  of  the  flower-garden  on  either  side  of  the  house,  and 
these  at  once  returned  to  the  hive ; and  with  repetition  of 
the  experiment,  a similar  result,  even  arriving  at  the  hive 
before  he  himself  had  time  to  run  from  the  place  where  he 
had  liberated  them  to  the  hive.  As  the  garden  was  a large 
one,  many  of  them  had  to  fly  a greater  distance,  in  order 
to  reach  the  hive,  than  those  liberated  on  the  front  lawn. 
Their  uniform  success,  therefore,  in  finding  their  way  home 
so  immediately  was  no  doubt  due  to  their  special  knowledge 


1 Saigey,  The  Unity  of  Natural  Phenomena,  p.  66. 


312 


INDUCTIVE  LOGIC 


of  the  flower-garden,  and  not  to  any  general  sense  of  direc- 
tion.1 

The  hypothesis  that  leads  to  verification  by  experiment 
represents  true  scientific  procedure,  and  that  which  has 
actually  been  the  most  effective  instrument  of  research  in 
all  the  various  spheres  of  human  investigation.  The  old 
controversy  between  Mill  and  Whewell  admits  of  a ready 
adjustment  in  this  regard.  Whewell  emphasized  discovery 
as  the  heart  of  the  system  of  induction,  leading  to  the  fram- 
ing of  hypotheses  whose  chief  test  was  not  experimental 
so  much  as  the  capability  of  accounting  for  the  given  phe- 
nomena. Mill,  on  the  other  hand,  insisted  that  logic  was 
essentially  proof,  and  not  discovery.  He,  accordingly, 
emphasized  the  experimental  testing  by  means  of  his  several 
methods,  as  being  the  all-important  part  of  the  inductive 
method.  He  had  little  concern  for  the  origin  of  the  sug- 
gestions as  to  the  most  likely  causal  elements  in  the  midst 
of  a complex  phenomenon.  The  primary  function  of 
logic,  according  to  him,  is  merely  to  prove  or  disprove. 
The  ideas  of  Whewell  and  Mill  are  not  necessarily  con- 
tradictory ; they  can  be  regarded  as  mutually  supplementary, 
which  gives  us  a true  account  of  the  ideal  logical  method, 
where  hypothesis  suggests  the  line  of  experiment,  and 
experiment  in  turn  confirms  hypothesis.  In  such  a method, 
as  can  be  seen  in  the  illustration  given,  there  is  a blending 
of  deductive  and  inductive  reasoning,  which  is  the  general 
characteristic  of  all  actual  processes  of  thought.  As  Sigwart 
has  so  admirably  put  it : “ Without  quickness  of  combina- 
tion, by  which  we  can  call  up  a number  of  possible  analogies 
and  apply  them  to  the  unexplained  case ; without  a happy 
power  of  divination  which  is  guided  by  unanalyzable  associa- 
tions to  discover  that  analogy  which  embraces  most  aspects 
of  the  event;  finally,  without  imagination  to  construct  con- 
nections for  which  the  only  ground  may  be  a hidden 

1 Lubbock,  On  the  Senses,  Instincts,  and  Intelligence  of  Animals,  pp. 
269,  270. 


HYPOTHESIS 


313 


similarity,  our  thoughts,  if  compelled  to  proceed  strictly 
according  to  method,  would  frequently  be  condemned,  by 
the  impossibility  of  discovering  in  this  way  a sufficiently 
grounded  connection,  to  complete  stagnation.  But  the  fact 
is  in  no  way  contrary  to  the  nature  of  induction ; it  is  a 
necessary  consequence  of  it.  We  cannot  even  begin  the 
process  of  inference  without  making  general  assumptions ; 
and  the  general  proposition  which  we  get  by  summing  up 
a number  of  instances  is  really  a hypothesis,  to  which,  it 
is  true,  we  are  led  clearly  and  certainly  in  this  case.  But 
between  these  most  general  presuppositions,  upon  which  all 
induction  is  grounded,  and  the  simplest  cases  to  which  they 
can  be  applied,  there  is  a wide  region  within  which  the 
hypotheses  which  are  always  necessary  for  induction  can 
only  be  formed  tentatively,  in  order  to  give  some  definite 
direction  to  investigation,  to  serve  in  our  analysis  of  phe- 
nomena into  their  elements  as  a means  of  breaking  up  com- 
plete phenomena  on  certain  lines,  and  to  invent  the 
experiments  which  will  make  it  possible  to  confirm  or 
refute  an  opinion.”  1 


1 Sigwart,  Logic,  Vol.  II,  p.  423. 


CHAPTER  XIII 


ANALOGY 

Analogy  as  we  have  seen  is  a process  of  inference  from 
a particular  case  to  a particular.1  Because  they  agree  in 
certain  respects,  it  is  inferred  that  they  will  agree  in  other 
respects  also.  Such  reasoning  admits  of  various  degrees  of 
cogency,  and  in  no  case  is  it  ever  completely  conclusive.  It 
may  give  rise  to  an  exceedingly  high  degree  of  probability, 
but  nothing  more.  However  the  conclusion  which  analogy 
suggests  as  extremely  probable  may  be  submitted  to  the 
tests  of  one  or  more  of  the  inductive  methods,  and  thereby 
be  satisfactorily  proved.  In  that  case,  the  particular  case 
which  was  the  starting-point  of  the  analogical  inference  can 
then  be  regarded  as  the  typical  case  which  ranks  as  repre- 
sentative of  the  universal  attained  by  the  inductive  inves- 
tigation. One  of  the  most  important  features  of  analogy 
is  that  while  incomplete  in  itself,  it  nevertheless  leads  by 
suggestion  to  inductive  experimentation  which  renders  it 
complete  or  else  discloses  its  points  of  weakness.  As  an 
instrument  of  discovery,  analogy  has  played  a very  impor- 
tant role  in  scientific  research.  In  1845  Faraday  discovered 
the  magnetic  rotary  polarization  of  light;  by  analogical 
reasoning,  Waitmann  in  the  following  year  inferred  that  a 
similar  result  would  be  attained  with  a beam  of  heat,  which 
was  afterwards  experimentally  verified. 

The  so-called  “natural  kinds”  furnish  manifold  illustra- 
tions of  analogies.  They  possess  numerous  properties,  some 
of  them  known  and  others  unknown.  Through  large  groups 
of  them  are  found  similar  characteristics  side  by  side  with 
1 See  p.  150. 

314 


ANALOGY 


315 


manifest  differences,  and  yet  the  similarities  are  so  striking 
that  often,  when  new  properties  are  discovered  in  certain 
members  of  the  group,  there  seems  to  be  ground  for  infer- 
ring their  existence  in  other  members  of  the  group  also. 
Certain  properties  known  to  exist  in  potassium  and  sodium 
were  inferred  to  be  present  in  rubidium  and  caesium  ; the 
carbonates  of  sodium  and  potassium  are  not  decomposed  by 
a red  heat,  and  it  was  inferred  that  the  same  would  prove 
true  of  the  carbonates  of  rubidium  and  caesium ; and  such 
proved  to  be  the  case.  Some  of  the  statements  which  are 
true  of  chlorine  are  found  to  be  true  of  bromine  and  iodine. 
Mr.  Gore,  having  found  the  molecular  change  in  antimony 
electro-deposited  from  its  chloride,  he  inferred  and  discov- 
ered the  same  in  that  deposited  from  its  bromide  and  iodide. 
Sir  Humphry  Davy,  having  discovered  that  potassium  might 
be  isolated  by  means  of  electrolysis,  immediately  inferred 
and  proceeded  to  prove  by  experiment  that  it  would  be 
possible  also  to  isolate  sodium  and  other  substances  having 
analogous  properties.1 

The  principle  of  analogy  lies  at  the  basis  of  all  classifica- 
tion, the  separating  and  grouping  together  in  appropriate 
divisions  individuals  which  possess  certain  salient  attributes 
in  common. 

Professor  Jevons’s  definition  of  classification  embodies  at 
the  same  time  a full  statement  of  its  exact  logical  signifi- 
cance as  an  instrument  of  research,  and  therefore  I give  it 
in  full:  “By  the  classification  of  any  series  of  objects  is 
meant  the  actual  or  ideal  arrangement  together  of  those 
which  are  alike,  and  the  separation  of  those  which  are 
unlike,  the  purpose  of  this  arrangement  being,  primarily, 
to  disclose  the  correlations  or  laws  of  union  of  proper- 
ties and  circumstances,  and  secondarily,  to  facilitate  the 
operations  of  the  mind  in  clearly  conceiving  and  retaining  in 
the  memory  the  characters  of  the  object  in  question."’2  In 

1 Gore,  The  Art  of  Scientific  Discovery,  p.  522. 

2 Jevons,  Principles  of  Science,  p.  677. 


316 


INDUCTIVE  LOGIC 


describing  the  purpose  of  classification,  the  latter  clause  is 
more  a psychological  desideratum  than  logical ; the  former 
specification  contains  its  logical  purpose ; namely,  to  dis- 
close the  correlations  or  laws  of  union  of  properties  and 
circumstances.  This  may  be  illustrated  in  the  grouping  to- 
gether of  potassium,  sodium,  caesium,  rubidium,  and  lithium, 
and  calling  them  the  alkaline  metals.  This  was  done  by 
virtue  of  the  common  characteristics  in  the  midst  of  their 
individual  peculiarities;  namely,  they  all  combine  very  en- 
ergetically with  oxygen  to  decompose  water  at  all  tempera- 
tures, and  form  strongly  basic  oxides,  which  are  highly 
soluble  in  water,  yielding  powerful  caustic  and  alkaline 
hydrates  from  which  water  cannot  be  expelled  by  heat ; their 
carbonates  are  also  soluble  in  water,  and  each  metal  forms 
only  one  chloride.  The  manifest  advantage  of  classifying 
these  metals  together  lies  in  its  suggestive  capacity,  as  we 
have  already  noted  in  illustrations  above  given.  So  many 
observed  similarities  suggest  inferences  by  analogy  ; when, 
for  instance,  a new  property  is  discovered  in  any  one  or  two 
of  the  metals  of  this  class,  the  idea  immediately  suggests 
itself  that  the  same  property  may  possibly  extend  over  all 
the  metals  of  the  same  class.  Not  only  is  such  an  idea 
suggested,  but  along  with  it  there  exists  an  antecedent 
probability  that  it  will  be  realized  actually. 

An  excellent  illustration  of  the  practical  results  attained 
through  a scientific  use  of  classification  is  found  in  Mr. 
Lockyer’s  researches  on  the  sun.1  As  a guide  to  the  ele- 
ments to  look  for  in  the  sun’s  photosphere,  he  prepared  a 
classification  of  elements  according  as  they  had  or  had  not 
been  traced  in  the  sun,  together  with  a detailed  statement 
of  the  chemical  nature  of  each  element.  He  was  then  able 
to  observe  that  the  elements  found  in  the  sun  were,  for  the 
most  part,  those  forming  stable  compounds  with  oxygen. 
He  then  inferred  that  the  other  elements  which  were  known 
to  form  stable  compounds  with  oxygen  would,  in  all  proba- 
1 Quoted  by  Jevons  in  Priticiples  of  Science,  p.  C76. 


ANALOGY 


317 


bility,  be  found  present  in  the  sun.  Starting  upon  this  sug- 
gested track,  he  succeeded  in  discovering  five  such  metals. 

Analogical  inference  carries  special  weight  when  it  is  based 
upon  the  principle  of  teleology ; that  is,  when  any  observed 
phenomena  seem  to  possess  structural  contrivances  adapted  to 
ends,  similar  in  some  degree  at  least  to  human  contrivances 
designed  to  produce  certain  proposed  ends.  When  this  simi- 
larity is  apparent,  it  suggests  the  possibility  that  an  observed 
contrivance  in  nature  may  subserve  ends  beyond  the  possi- 
bility of  observation,  and  which,  therefore,  may  be  inferred 
really  to  exist.  We  have  seen  that  the  ground  of  all  inference 
lies  in  the  representation  of  any  given  phenomena  of  con- 
sciousness as  cohering  in  one  system,  which  comprehends  the 
several  parts  in  a common  unity  of  such  a nature  that,  know- 
ing some  of  the  parts  and  their  relations,  we  infer  the  charac- 
ter and  function  of  other  parts  not  known,  and  yet  which  that 
already  known  necessitates.  And  among  the  many  kinds 
of  relation  that  may  obtain  between  part  and  part,  or  part 
and  whole,  the  teleological  is  a very  common  one;  and, 
moreover,  by  its  nature  necessitates  certain  consequences 
that  lie  beyond  the  sphere  of  observation,  and  yet,  never- 
theless, may  very  properly  be  supplied  by  inference.  In 
other  words,  the  causal  connections  in  a system  are  not 
merely  those  of  an  efficient  or  a formal  cause ; they  may, 
with  a like  force  and  suggestiveness,  be  considered  in  the 
light  of  a final  cause  ; that  is,  the  presence  of  means  adapted 
to  certain  ends,  or  of  organs  adapted  to  certain  necessary 
functions,  or  of  contrivances  of  a mechanical  nature  as 
though  designed  for  a specific  purpose. 

Janet  has  specially  emphasized  the  importance  and  prev- 
alence of  this  kind  of  inference,  and,  as  an  illustration  of 
the  cogency  of  inference  based  upon  finality,  he  urges  that 
the  certitude  which  the  belief  in  the  intelligence  of  our 
fellow-men  gives  us  is  based  upon  analogical  reasoning  of 
this  type ; and  that,  moreover,  this  belief,  resting  upon  such 
a basis,  is  one  of  the  strongest  beliefs  which  we  possess. 


318 


INDUCTIVE  LOGIC 


He  says:  “Now,  if  we  ask  ourselves  why  we  suppose  that 
other  men  think,  we  shall  see  that  it  is  in  virtue  of  the 
principle  of  final  causes.  In  effect,  what  is  it  that  experi- 
ence shows  in  the  actions  of  other  men,  but  a certain  num- 
ber of  phenomena  coordinated  in  a certain  manner,  and 
bound  not  only  together,  but  also  to  a future  phenomenon 
more  or  less  remote  ? Thus,  when  we  see  a man  prepare 
his  food  by  means  of  fire,  we  know  that  this  assemblage  of 
phenomena  is  connected  with  the  act  of  taking  food ; when 
we  see  a painter  drawing  lines  on  a canvas,  we  know  that 
these  apparently  arbitrary  acts  are  connected  with  the  exe- 
cution of  a picture  ; when  we  see  a deaf  mute  making  signs 
which  we  do  not  understand,  we  believe  that  these  gestures 
are  connected  with  a final  effect,  which  is  to  be  understood 
by  him  to  whom  he  makes  them;  in  fine,  when  men  speak, 
we  see  that  the  articulations  of  which  a phrase  is  composed 
are  coordinated  to  each  other  so  as  to  produce  a certain  final 
effect,  which  is  to  awaken  in  us  a certain  thought  and  senti- 
ment. Now  we  cannot  see  such  coordinations,  whether  actual 
or  future,  without  supposing  a certain  cause  for  them ; and 
as  we  know  by  internal  experience  that  with  ourselves  such 
coordinations  only  take  place  under  the  condition  that  the 
final  effect  is  previously  represented  in  our  consciousness, 
we  suppose  the  same  thing  in  the  case  of  other  men ; in  a 
word,  we  suppose  for  them  the  consciousness  of  an  end,  a con- 
sciousness reflecting  more  or  less,  according  as  the  circum- 
stances more  or  less  resemble  those  that  accompany  in 
ourselves  the  reflecting  consciousness.  Thus  when  we  affirm 
the  intelligence  of  other  men,  we  affirm  a truth  of  indisputa- 
ble certitude;  and  yet  we  only  affirm  it  on  the  ground  of 
analogy,  and  of  analogy  guided  by  the  principle  of  final 
causes.” 1 

In  this  illustration  of  Janet’s  we  have  the  idea  of  a system 
of  coordinated  parts  especially  prominent ; and  for  a satis- 
factory account  of  the  relations  obtaining  in  such  a system, 
1 Janet,  Final  Causes,  pp.  113,  114. 


ANALOGY 


319 


it  will  be  seen  how  indispensable  it  is  to  postulate  the  theory 
of  final  cause.  This  mode  of  inference  finds  a striking 
illustration  in  the  famous  discovery  of  Harvey,  concerning 
the  circulation  of  the  blood.  In  the  early  part  of  the 
seventeenth  century,  while  Harvey  was  his  pupil,  the  cele- 
brated anatomist,  Fabricius  Aquapendente  of  Padua,  ob- 
served that  many  veins  contain  valves  which  lie  open  as 
long  as  the  blood  is  flowing  toward  the  heart.  Harvey, 
learning  of  this  fact,  saw  in  it  the  suggestion  of  an  adapta- 
tion of  means  to  an  end ; namely,  a contrivance  so  fashioned 
by  nature  as  to  permit  the  blood  to  flow  always  in  one  direc- 
tion only,  and  to  prevent  its  flow  in  an  opposite  direction. 
Observation  of  other  portions  of  the  circulatory  mechanism 
led  to  a confirmation  of  the  idea,  and  to  the  discovery  of  the 
circulation  of  the  blood.1 

Again,  many  flint  substances  have  been  discovered,  as 
though  curiously  wrought  with  sharp  edges,  and  a place 
as  though  designed  for  a handle  with  which  to  wield  the 
stone  as  a weapon  or  a tool ; it  has  been  inferred  from  these 
general  characteristics  that  the  stones  were  so  constructed 
by  human  effort,  and  used  by  human  beings  for  the  purposes 
for  which  they  evidently  seem  to  be  adapted.  This  infer- 
ence is  based  upon  an  analogy  between  the  peculiar  shapes 
of  such  stones,  and  known  shapes  designed  and  used  by 
man. 

This  form  of  analogy  has  proved  especially  suggestive  in 
researches  regarding  plant  and  animal  life.  Sir  John  Lub- 
bock gives  the  following  description  of  the  common  white 
dead-nettle  with  the  explanation  of  its  functions  that  is 
evidently  a teleological  inference : “ The  flower  consists 
of  a narrow  tube,  somewhat  expanded  at  the  upper  end, 
where  the  lower  lobe  of  the  corolla  forms  a platform,  on 
each  side  of  which  is  a small  projecting  lobe.  The  upper 
portion  of  the  corolla  is  an  arched  hood,  under  which  lie 
four  anthers  in  pairs,  while  between  them  and  projecting 
1 Gore,  Art  of  Scientific  Discovery,  p.  571. 


320 


INDUCTIVE  LOGIC 


somewhat  downwards  is  the  pointed  pistil.  At  the  lower 
end,  the  tube  contains  honey,  and  above  the  honey  is  a row 
of  hairs  almost  closing  the  tube.  Now,  why  has  the  flower 
this  peculiar  form  ? What  regulates  the  length  of  the  tube  ? 
What  is  the  use  of  this  arch  ? What  lessons  do  these  lobes 
teach  us  ? What  advantage  is  the  honey  to  the  flower  ? 
Of  what  use  is  the  fringe  of  hairs?  Why  does  the  stigma 
project  beyond  the  anthers  ? Why  is  the  corolla  white, 
while  the  rest  of  the  plant  is  green  ? Similar  questions 
may  of  course  be  asked  with  reference  to  other  flowers.  At 
the  close  of  the  last  century,  Conrad  Sprengel  published  a 
valuable  work,  in  which  he  pointed  out  that  the  forms  and 
colors,  the  scent,  honey,  and  general  structure  of  flowers, 
have  reference  to  the  visits  of  insects,  which  are  of  impor- 
tance in  transferring  the  pollen  from  the  stamens  to  the 
pistil.  Mr.  Darwin  developed  this  theory  and  proved  ex- 
perimentally that  the  special  service  which  insects  perform 
to  flowers,  consists  not  only  in  transferring  the  pollen  from, 
the  stamens  to  the  pistil,  but  in  transferring  it  from  the 
stamens  of  one  flower  to  the  pistil  of  another.” 1 The  line 
of  subsequent  observation  and  experiment  was  thus  origi- 
nally suggested  by  the  structural  appearance  of  these  flowers 
which  seemed  formed  for  some  specific  end.  The  questions, 
once  started,  — To  what  end?  To  what  purpose?  For 
what  use  ? — led  to  the  theory  of  Sprengel  and  the  corrobo- 
rative experiments  of  Darwin. 

This  is  further  illustrated  in  some  very  interesting  flower 
structures,  also  described  by  Sir  John  Lubbock,  which  indi- 
cate peculiar  contrivances  for  the  destruction  of  insects. 
The  peculiarity  of  formation  first  suggested  some  such 
end  as  this,  which  has  since  been  proved  by  careful  observa- 
tion to  be  the  case.  “ The  first  observation  on  insect-eating 
flowers  was  made  about  the  year  1868  by  Ellis.  He  ob- 
served that  in  Dionvea,  a North  American  plant,  the  leaves 
have  a joint  in  the  middle,  and  thus  close  over,  kill,  and 
1 Lubbock,  Scientific  Lectures,  pp.  1,  2. 


ANALOGY 


321 


actually  digest  any  insect  which  may  alight  on  them.  An- 
other case  is  that  of  Utricularia,  an  aquatic  species  which 
bears  a number  of  utricles  or  sacs,  which  have  been  sup- 
posed to  act  as  floats.  Branches,  however,  which  bear  no 
bladders  float  just  as  well  as  the  others,  and  there  seems  no 
doubt  that  their  real  use  is  to  capture  small  aquatic  animals, 
which  they  do  in  considerable  numbers.  The  bladders,  in 
fact,  are  on  the  principle  of  an  eel-trap,  having  an  entrance 
closed  with  a flap,  which  permits  an  easy  entrance,  but 
effectually  prevents  the  unfortunate  victim  from  getting 
out  again.  In  the  genus,  Sarracenia,  some  of  the  leaves  are 
in  the  form  of  a pitcher.  They  secrete  a fluid,  and  are  lined 
internally  with  hairs  pointing  downwards.  Up  the  outside 
of  the  pitcher  there  is  a line  of  honey  glands  which  lure  the 
insects  to  their  destruction.  Flies  and  other  insects  which 
fall  into  this  pitcher  cannot  get  out  again  and  are  actually 
digested  by  the  plant.” 1 

In  the  example  where  the  idea  of  an  eel-trap  suggested 
the  possible  function  of  the  similar  structure  in  the  plant, 
Utricularia,  we  find  one  of  the  most  striking  illustrations 
of  this  mode  of  analogical  inference.  It  was  an  easy  and 
natural  transition  from  similarity  of  structure  to  similarity 
of  function.  To  give  an  idea  of  the  great  number  of  teleo- 
logical phenomena  in  the  vegetable  and  animal  world,  and 
the  wealth  of  possible  suggestion  stored  away  in  these 
various  structures,  and  disclosed  by  a sagacious  analysis,  I 
quote  a remark  of  Sir  John  Lubbock’s  in  commenting  upon 
the  variation  of  color  and  markings  of  caterpillars : “ I should 
produce  an  impression  very  different  from  that  which  I 
wish  to  convey,  were  I to  lead  you  to  suppose  that  all  these 
varieties  have  been  explained  or  are  understood.  Far  from 
it ; they  still  offer  a large  field  for  study ; nevertheless,  I 
venture  to  think  the  evidence  now  brought  forward,  how- 
ever imperfectly,  is  at  least  sufficient  to  justify  the  conclu- 
sion that  there  is  not  a hair  or  a line,  not  a spot  or  a color, 

1 Lubbock,  Scientific  Lectures,  pp.  4,  5. 


322 


INDUCTIVE  LOGIC 


for  which  there  is  not  a reason,  — which  has  not  a purpose 
or  a meaning  in  the  economy  of  nature.”  1 

An  illustration  given  by  Darwin  shows  this  mode  of  in- 
ference applied  to  the  sphere  of  animal  life  also.  He  says : 
“ The  great  size  of  the  bones  of  the  megatherioid  animals 
was  a complete  puzzle  to  naturalists  until  Professor  Owen 
lately  solved  the  problem  with  remarkable  ingenuity.  The 
teeth  indicate,  by  their  simple  structure,  that  these  mega- 
therioid animals  lived  on  vegetable  food,  and  probably  on 
the  leaves  and  small  twigs  of  trees ; their  ponderous  forms 
and  great,  strong,  curved  claws  seem  so  little  adapted  for 
locomotion  that  some  eminent  naturalists  have  actually  be- 
lieved that,  like  the  sloths,  to  which  they  are  intimately 
related,  they  subsisted  by  climbing  back  downwards  on 
trees,  and  feeding  on  the  leaves.  It  was  a bold,  not  to  say 
preposterous,  idea,  to  conceive  even  antediluvian  trees  with 
branches  strong  enough  to  bear  animals  as  large  as  ele- 
phants. Professor  Owen,  with  far  more  probability,  be- 
lieves that,  instead  of  climbing  on  the  trees,  they  pulled 
the  branches  down  to  them,  and  tore  up  the  smaller  ones  by 
the  roots,  and  so  fed  on  the  leaves.  The  colossal  breadth 
and  weight  of  their  hinder  quarters,  which  can  hardly  be 
imagined  without  having  been  seen,  become,  on  this  view, 
of  obvious  service,  instead  of  being  an  encumbrance : their 
apparent  clumsiness  disappears.  With  their  great  tails  and 
their  huge  heels  firmly  fixed  like  a tripod  on  the  ground, 
they  could  freely  exert  the  full  force  of  their  most  powerful 
arms  and  great  claws.  Strongly  rooted,  indeed,  must  have 
been  that  tree  which  could  have  resisted  such  force ! The 
Mylodon,  moreover,  was  furnished  with  a long  extensile 
tongue  like  that  of  the  giraffe,  which,  by  one  of  those  beau- 
tiful provisions  of  nature,  thus  reaches,  with  the  aid  of  its 
long  neck,  its  leafy  food.”2  Throughout  we  observe  ana- 
logical inference  based  upon  these  teleological  marks,  and 
furnishing  a basis  for  a satisfactory  hypothesis. 

1 Lubbock,  Scientific  Lectures,  pp.  60,  67. 

2 Darwin,  Voyage  of  a Naturalist,  pp.  106,  107. 


ANALOGY 


323 


We  see  what  a wide  field  thus  opens  in  the  region  of 
biology  alone  for  the  discovery  of  resemblances  leading  to 
the  appreciation  of  the  fuller  teleological  significance  of 
plant  and  animal  life. 

In  the  illustrations  given,  both  of  the  teleological  and 
other  forms  of  analogy,  we  notice  that  its  chief  logical  func- 
tion is  that  of  suggestion  of  some  hypothesis  which  may  or 
may  not  be  afterwards  confirmed  by  subsequent  experiment. 
Some  of  the  most  important  discoveries  of  science  have 
arisen  from  analogical  suggestions.  Sir  John  Herschel  was 
led  by  observed  analogies  to  predict  certain  phenomena 
afterwards  verified  experimentally  by  Faraday.  Herschel 
had  noticed  that  a screw-like  form,  known  as  helicoidal  dis- 
symmetry, was  observed  in  three  cases,  namely,  in  electrical 
helices,  plagihedral  quartz  crystals  (that  is,  crystals  having  an 
oblique  spiral  arrangement  of  planes),  and  the  rotation  of  the 
plane  of  polarization  of  light.  As  Herschel  himself  said : 
“ I reasoned  thus  : Here  are  three  phenomena  agreeing  in  a 
very  strange  peculiarity.  Probably  this  peculiarity  is  a con- 
necting link,  physically  speaking,  among  them.  How,  in 
the  case  of  the  crystals  and  the  light,  this  probability  has 
been  turned  into  certainty  by  my  own  experiments.  There- 
fore, induction  led  me  to  conclude  that  a similar  connection 
exists,  and  must  turn  up,  somehow  or  other,  between  the 
electric  current  and  polarized  light,  and  that  the  plane  of 
polarization  would  be  defected  by  magneto-electricity.” 
Herschel  thus  anticipated  Faraday’s  experimental  discovery 
of  the  influence  of  magnetic  strain  upon  polarized  light.1 

Another  important  discovery  — the  germ-theory  of  epi- 
demic disease  — was  first  suggested  by  an  analogy.  In  the 
theory,  as  expressed  by  Kircher,  and  favored  by  Linnaeus, 
and  afterwards  supported  by  Sir  Henry  Holland,  its  special 
strength,  according  to  Professor  Tyndall,  “ consisted  in  the 
perfect  parallelism  of  the  phenomena  of  contagious  disease 
with  those  of  life.  As  a planted  acorn  gives  birth  to  an 
1 Jevons,  Principles  of  Science,  p.  630. 


324 


INDUCTIVE  LOGIC 


oak  competent  to  produce  a whole  crop  of  acorns,  each  gifted 
with  the  power  of  reproducing  the  parent  tree,  and  as  thus 
from  a single  seedling  a whole  forest  may  spring,  so,  it  is 
contended,  these  epidemic  diseases  literally  plant  their  seeds, 
grow  and  shake  abroad  new  germs,  which,  meeting  in  the 
human  body  their  proper  food  and  temperature,  finally  take 
possession  of  whole  populations.” 1 

The  theory  of  evolution  was  first  suggested  to  Mr.  Darwin 
by  the  analogous  phenomena  observed  in  artificial  selection 
and  breeding.  The  transition  to  natural  selection  was  easily 
made,  especially  as,  on  reading  Malthus,  On  Population,  he 
conceived  the  idea  of  a struggle  for  existence  as  the  inevi- 
table result  of  the  rapid  increase  of  organic  beings.  This 
idea  necessitated  the  natural  selection,  which  he  needed  to 
account  for  results  similar  to  the  artificial  selection,  and 
thus  his  theory  grew  out  of  an  analogy  as  its  beginning. 
Moreover,  in  the  development  of  the  theory  in  its  manifold 
details,  other  analogies  proved  also  suggestive.  For  in- 
stance, there  is  the  supposed  analogy  between  the  growth 
of  a species  and  the  growth  of  an  individual.  It  supposes, 
for  example,  as  Professor  Clifford  has  put  it,  “that  the  race 
of  crabs  has  gone  through  much  the  same  sort  of  changes  as 
every  crab  goes  through  now,  in  the  course  of  its  formation 
in  the  egg,  — changes  represented  by  its  pristine  shape 
utterly  unlike  what  it  afterwards  attains,  and  by  its  gradual 
metamorphosis  and  formation  of  shell  and  claws.” 2 

The  germ-theory  of  putrefaction,  first  suggested  by 
Schwann,  received  confirmation  through  certain  resem- 
blances noted  by  Professor  Lister  between  fermentation 
and  putrefaction.  In  his  Introductory  Lecture  before  the 
University  of  Edinburgh,  Professor  Lister  called  attention 
to  the  fact  that  fermentation  and  putrefaction  present  a 
very  striking  parallel.  In  each  a stable  compound  — sugar 
in  one  case,  albumen  in  the  other  — undergoes  extraordi- 

1 Tyndall,  Fragments  of  Science,  p.  287. 

2 Clifford,  Lectures  and  Essays,  p.  86. 


ANALOGY 


325 


nary  chemical  changes  under  the  influence  of  an  excessively 
minute  quantity  of  a substance  which,  regarded  chemically, 
would  be  considered  inert.  It  was  pointed  out  also  by 
Professor  Lister  in  this  connection,  that,  as  was  well 
known,  one  of  the  chief  peculiarities  of  living  organisms 
is  that  they  possess  extraordinary  powers  of  effecting 
chemical  changes  in  materials  in  their  vicinity  out  of  all 
proportion  to  their  energy  as  mere  chemical  compounds. 
Such  being  the  facts  in  the  case,  and,  moreover,  the  fermen- 
tation of  sugar  being  generally  allowed  to  be  occasioned  by 
the  presence  of  living  organisms,  Professor  Lister’s  infer- 
ence was  that  putrefaction  was  due  to  an  analogous 
agency.1 

A discovery  in  quite  a different  sphere,  that  of  mathe- 
matics, leading  to  the  branch  of  analytical  geometry,  was 
first  suggested  to  Descartes  through  observing  the  resem- 
blances existing  between  geometry  and  algebra.  In  a sim- 
ilar manner,  Boole  was  led,  by  the  resemblances  noted 
between  algebra  and  logic,  to  give  expression  to  the  same 
in  a system  which  he  called  the  laws  of  thought,  and  which 
has  become  the  basis  of  a general  or  symbolic  logic. 

While  there  are  thus  unquestionable  evidences  of  the 
value  of  analogy  as  a form  of  inference,  there  are  also  cases 
of  false  analogy  unfortunately  so  numerous  as  to  discredit 
the  process  wholly  in  some  quarters.  It  will  be  well,  there- 
fore, to  indicate  some  of  the  requirements  of  true  analogy  : — 

1.  In  the  first  place  the  resemblance  must  be  a prepon- 
derating one ; that  is,  the  phenomena  compared  must  show 
a more  striking  agreement  than  difference.  Some  writers 
have  balanced  agreement  against  difference  upon  a purely 
numerical  basis  of  comparison,  forming  what  may  be 
called  an  analogical  ratio,  with  points  of  similarity  forming 
the  numerator,  and  the  points  both  of  similarity  and  dif- 
ference, plus  the  unknown,  that  is,  the  total  number,  form- 
ing the  denominator.  Such  a representation  of  the  force  of 
1 Tyndall,  Fragments  of  Science,  pp.  300-302. 


326 


INDUCTIVE  LOGIC 


an  analogy  is  given  by  Mill,  Bain,  and  others.  I think, 
however,  that  this  representation  is  apt  to  be  misleading 
in  producing  the  impression  that  the  mere  number  of  points 
of  agreement,  irrespective  of  their  significance,  is  the  chief 
feature  of  analogy.  Whereas  it  is  the  weight  of  the  agree- 
ing attributes,  and  not  the  number,  that  counts.  As  has 
been  before  said,  in  analogy  we  weigh  instances,  and 
do  not  count  them.  The  analogical  ratio  expressed  nu- 
merically, as  above,  is  really  equivalent  to  the  ratio  of 
probability  which  will  be  described  in  the  following  chap- 
ter. I have  therefore  changed  the  usual  wording  of  this 
requirement,  so  that  it  reads,  the  resemblances  must  be 
more  striking  and  more  significant  than  the  differences. 
This  provides  for  cases  when  perhaps  a few  points  of  resem- 
blance will  be  of  such  a nature  as  to  outweigh  many  points 
of  difference  in  the  total  estimate. 

This  requirement  also  excludes  all  fanciful  analogies  and 
all  resemblances  resting  upon  a figurative  rather  than  a real 
basis.  For  instance,  the  advocates  of  annual  Parliaments 
in  the  time  of  the  Commonwealth,  urged  their  case  on  the 
analogical  ground  that  a body  politic  is  similar  to  a living 
body  and  that  serpents  annually  cast  their  skin,  which, 
being  no  doubt  for  a beneficial  purpose,  might  well  be 
imitated. 

2.  In  noting  the  points  of  resemblance  between  two  phe- 
nomena, all  circumstances  which  are  known  to  be  effects  of 
one  cause  must  therefore  be  regarded  not  as  many,  but  as 
one.  For  instance,  two  chemical  oxides  may  be  compared; 
the  effects  common  to  each  may  be  due  to  the  presence  of 
the  oxygen  which  each  contains,  and  therefore  must  not  be 
regarded  in  the  light  of  independent  marks  of  similarity. 

3.  If  we  infer  by  analogy  that  a substance  possesses  a 
certain  property  which  we  know  is  incompatible  with  some 
one  or  other  known  properties  of  the  substance,  the  analogy 
is  at  once  discredited.  We  may  infer  that  the  moon  is 
inhabited,  by  virtue  of  the  many  points  of  resemblance 


ANALOGY 


327 


between  the  moon  and  the  earth.  However,  the  fact  that 
the  moon  has  no  atmosphere  necessary  to  sustain  life,  at 
once  makes  such  an  argument  based  upon  analogy  wholly 
out  of  the  question. 

4.  There  are  certain  special  requirements  referring  to 
that  particular  form  of  analogy  which  is  based  upon  teleo- 
logical considerations.  They  are  as  follows  : — 

a.  This  principle  must  never  be  used  as  an  argument 
against  an  observed  fact,  or  an  established  law  of  nature. 
While  this  precaution  is  not  necessary  at  the  present  time, 
in  scientific  circles  at  least,  still  there  was  a time  when  its 
counsel  was  sorely  needed.  When  in  astronomy  it  was 
proved  that  there  were  suns  gravitating  around  other  suns, 
without  our  solar  system,  this  was  objected  to  upon  the  fol- 
lowing ground,  as  given  by  one  Nicholas  Fuss,  a celebrated 
astronomer,  at  the  end  of  the  eighteenth  century:  “ What  is 
the  good  of  some  luminous  bodies  revolving  round  others  ? 
The  sun  is  the  only  source  whence  the  planets  derive  light 
and  heat.  Were  their  entire  systems  of  suns  controlled  by 
other  suns,  their  neighborhood  and  their  motions  would  be 
objectless,  their  rays  useless.  The  suns  have  no  need  to  bor- 
row from  strange  bodies  what  they  themselves  have  received 
as  their  own.  If  the  secondary  stars  are  luminous  bodies, 
what  is  the  end  of  their  motives  ? ” 

There  is,  moreover,  another  abuse  of  the  principle  of  final 
causes,  which  has  also  historic  interest  rather  than  any 
present  pertinence ; namely,  opposing  certain  false  teleolog- 
ical ideas  to  established  discoveries  or  inventions,  with  a 
mistaken  zeal,  in  defence  of  a Divine  Providence.  For 
instance,  at  the  time  of  Jenner’s  great  discovery,  an  English 
physician,  Dr.  Rowley,  said  of  smallpox : “ It  is  a malady 
imposed  by  the  decree  of  heaven,  and  vaccination  is  an 
audacious  and  sacrilegious  violation  of  our  holy  religion. 
The  designs  of  these  vaccinators  appear  to  defy  heaven 
itself,  and  the  very  will  of  God.”  The  introduction  of 
winnowing  machines  into  Scotland  met  with  bitter  oppo- 


328 


INDUCTIVE  LOGIC 


sition  on  the  ground  that  the  winds  were  the  work  of 
God,  and  that  the  wind  thus  artificially  raised  was  a ver- 
itable “ devil’s  wind,”  as  they  were  wont  to  call  it.  Sir 
Walter  Scott,  in  Old  Mortality,  has  the  old  Mause  say  to 
her  mistress  : “ Your  ladyship  and  the  steward  are  wishing 
Cuddie  to  use  a new  machine  to  winnow  the  corn.  This 
machine  opposes  the  designs  of  Providence,  by  furnishing 
wind  for  your  special  use,  and  by  human  means,  in  place  of 
asking  it  by  prayer,  and  waiting  with  patience  till  Provi- 
dence itself  sends  it.” 

b.  Final  causes  should  never  be  employed  to  explain  phe- 
nomena which  do  not  exist.  As  M.  Florens  has  said:  “We 
must  proceed  not  from  final  causes  to  facts,  but  from  facts 
to  final  causes ; that  is,  we  should  not  superimpose  final 
causes  upon  phenomena.  We  must  see  them  in  phenomena 
themselves,  and  we  must  not  arbitrarily  project  a teleologi- 
cal idea,  purely  subjective,  upon  an  objective  ground.  ' Thus 
in  ancient  times,  Hippocrates  is  said  to  ‘ have  admired  the 
skill  with  which  the  auricles  of  the  heart  have  been  made 
to  blow  the  air  into  the  heart.’  ” 

c.  We  must  distinguish  accidental  from  essential  marks 
of  finality,  and  not  be  led  into  fanciful  or  far-fetched  anal- 
ogies. Voltaire  has  expressed  such  a defect  when  in  satire 
he  made  that  famous  remark,  “Noses  are  made  in  order  to 
bear  spectacles.” 

Bernardin  de  Saint-Pierre  says : “ Dogs  are  usually  of  two 
opposite  colors,  the  one  light,  the  other  dark,  in  order  that 
whenever  they  may  be  in  the  house,  they  may  be  distinguished 
from  the  furniture,  with  the  color  of  which  they  might  be 
confounded.  . . . Wherever  fleas  are  they  jump  on  white 
colors.  This  instinct  has  been  given  them,  that  we  may  the 
more  easily  catch  them.”  And  again  the  same  waiter  says : 
“ The  melon  has  been  divided  into  sections  by  nature,  for 
family  eating.” 1 All  such  grotesque  inferences  will  give 

1 The  illustrations  upon  the  abuse  of  final  causes  I have  taken  from 
Janet’s  admirable  chapter,  — Chapter  VIII  of  Appendix. 


ANALOGY 


329 


an  idea  of  how  readily  the  imagination  will  run  riot  if 
allowed  to  remain  uncurbed  by  the  reason. 

5.  Analogy  should  never  be  regarded  as  having  more 
weight  than  that  of  extremely  high  probability,  even  in 
cases  seemingly  most  conclusive.  Its  true  function  as  we 
have  seen  is  suggestive,  leading  to  hypothesis  and  experi- 
ment, and  it  needs  this  supplementary  proof.  It  was  an 
inference  based  on  analogy,  for  instance,  which  suggested 
the  probability  that  the  Binomial  Law,  having  proved  to 
be  valid  as  regards  the  second,  third,  and  fourth  powers, 
might  also  be  extended  to  the  fifth,  and  so  on  to  the  other 
powers  indefinitely.  This  suggestion  offered  no  real  basis, 
however,  upon  which  the  Binomial  Theorem  could  rest ; it 
needed  mathematical  demonstration  to  confirm  and  general- 
ize its  expression  in  the  special  cases  already  experimentally 
tested,  so  as  to  cover  all  possible  exponents,  both  positive 
and  negative,  fractional  and  integral. 

So  also  the  discovery  of  the  circulation  of  the  blood  was 
first  suggested  to  Harvey,  as  has  been  said,  by  analogical 
considerations  upon  observed  teleological  phenomena.  Har- 
vey, however,  was  not  content  with  this  suggestion  merely. 
He  was  led  to  experiment  upon  the  veins  and  arteries ; he 
tied  an  artery  and  vein,  and  carefully  observed  the  mechani- 
cal effects  upon  the  two  sides  of  the  tied  parts.  Experi- 
ments of  this  nature,  with  close  observation  and  study, 
were  kept  up  most  diligently,  and  with  rare  perseverance, 
for  nineteen  years,  before  he  had  traced  the  entire  course 
of  the  blood  through  all  parts  of  the  human  body,  and,  in 
a manner  wholly  satisfactory  to  himself,  verified  the  first 
statement  of  this  theory. 


CHAPTER  XIV 


PROBABILITY 

There  are  certain  phenomena  of  such  a nature  that  their 
antecedents,  being  extremely  complex,  cannot  be  adequately 
comprehended  by  observation,  however  searching  it  may  be ; 
nor  can  they  be  subjected  to  any  analysis  that  will  disclose 
the  causal  elements  to  which  the  effect  in  question  is  due. 
Moreover,  with  seemingly  the  same  antecedents,  the  event 
sometimes  happens,  and  sometimes  does  not ; and  even  with 
antecedents  associated  with  an  event  as  cause  and  effect 
respectively,  nevertheless  the  event  does  not  occur  as  we 
should  naturally  expect,  while  with  antecedents  associated 
with  the  contradiction  of  the  event  as  cause  and  effect 
respectively,  we  find  the  occurrence  of  the  event  quite 
contrary  to  what  we  should  naturally  expect.  The  evi- 
dence of  a constant  connection  between  antecedent  and 
consequent,  that  we  have  found  in  so  many  cases  which  we 
have  examined,  is  here  wholly  lacking.  Regularity  has 
been  replaced  by  irregularity  respecting  such  phenomena. 
For  instance,  I throw  dice  repeatedly;  the  antecedent 
shaking  of  the  box,  and  tossing  the  dice  upon  the  table, 
is  about  the  same  each  time,  at  least  the  difference  can- 
not be  determined,  and  yet  the  results  vary  with  each 
successive  throw.  The  causal  determination  in  each  case  is 
so  complex  as  to  be  beyond  computation;  the  initial  posi- 
tion of  the  dice,  the  force  of  their  ejection  from  the  box, 
the  height  of  the  box  above  the  table  when  they  leave  it, 
the  inequalities  of  the  table  itself,  a variation  between  the 
physical  and  geometrical  centres  of  gravity  of  the  dice,  etc., 
all  these  make  the  antecedent  so  complex  that  a slight  vari- 

330 


PROBABILITY 


331 


ation  in  any  one  of  these  conditions  will  affect  the  result. 
We  find,  therefore,  double  sixes  at  one  time,  a three  and 
four  at  another,  and  so  on  indefinitely. 

Or,  again,  it  sometimes  happens  that  with  perfect  sanitary 
conditions  a contagious  disease  will  appear,  that  has  always 
been  regarded,  and  that  correctly,  as  due  to  imperfect  sani- 
tation ; or,  an  entire  disregard  of  sanitary  requirements  and 
of  all  the  laws  of  health  may  yet  give  rise  to  no  disease  of 
special  moment.  Certain  conditions  of  temperature,  atmos- 
pheric pressure,  velocity  and  direction  of  the  wind,  may  one 
day  bring  storm  and  rain,  and  as  far  as  observation  can 
detect,  similar  conditions  may  again  bring  fair  weather. 
So,  also,  the  rise  and  fall  in  stock  and  money  markets  is 
extremely  susceptible  to  the  varying  conditions  of  indefi- 
nitely complex  forces  wholly  beyond  all  powers  of  deter- 
mination or  of  prediction.  Such  phenomena  present  a 
problem  which  the  methods  of  inductive  inquiry  cannot 
deal  with.  Observation  is  not  far-reaching  enough  to  pro- 
vide the  data  for  the  solution  of  the  problem,  and,  even  if 
it  were,  our  methods  of  computation  and  determination  are 
not  sufficiently  adequate  to  solve  problems  of  so  many  terms 
and  of  so  complex  a nature. 

The  experimental  methods  are  designed  to  test  causes 
suggested  by  analogy,  or  by  mental  analysis;  but  in  such 
phenomena  as  these,  the  problem  is  not  simply  to  find  a 
causal  connection.  The  causal  connection  may  be  estab- 
lished beyond  all  reasonable  doubt,  and  yet  the  cause  ob- 
tains in  the  midst  of  so  complex  a setting  that  the  problem 
is  really  this,  — to  determine  whether  a cause,  whose  exact 
nature  may  be  known  or  unknown,  will  prove  operative  or 
inoperative.  The  cause  may  be  always  present  and  even  its 
exact  nature  may  be  known,  and  yet  the  complex  circum- 
stances attending  it  may  be  of  such  a character  that  one 
alone,  or  two  or  more  combining,  may  neutralize  the  opera- 
tion of  the  cause,  and  on  the  other  hand  a slight  variation 
of  the  combined  circumstances  may  promote  and  even 


832 


INDUCTIVE  LOGIC 


accelerate  the  operation  of  the  cause  in  question.  The 
problem  then  is  to  determine  how  often  the  event  happens, 
and  how  often  it  fails  of  happening,  the  complex  and  in- 
determinate antecedent  being  present  in  all  the  instances 
examined. 

When  we  begin  to  count  instances,  we  are  reminded  that 
we  must  be  in  the  near  neighborhood  of  the  sphere  of 
enumerative  induction.  Enumerative  induction,  it  will 
be  remembered,  treats  instances  by  noting  the  number  of 
observed  coincident  happenings  of  the  antecedent  and  con- 
sequent under  investigation,  no  attempt  being  made  to 
analyze  their  respective  contents,  or  to  determine  a causal 
connection  more  definitely  by  means  of  any  one  or  more  of 
the  inductive  methods  of  research  and  verification.  The 
result  of  such  an  investigation  may  be  formulated  in  a 
proposition  of  the  form,  Every  A is  B.  This,  strictly  inter- 
preted, has  the  force  of,  Every  A that  has  been  observed  is 
B.  The  enumeration  of  the  kind  of  instances  which  we  are 
discussing  in  this  chapter,  however,  differs  from  this  in 
that  the  observation  leads  to  a twofold  result,  — a set 
of  instances  in  which  it  is  observed  that  the  _4’s  are  B’s 
also,  another  set  however  in  which  the  ,4’s  are  not  B’s. 
These  instances  are  of  such  a nature  that  the  observed  A 
is  an  antecedent  so  extremely  complex  that  the  element 
within  it,  which  is  a cause  capable  of  producing  B,  may 
either  be  absent  without  producing  an  appreciable  change 
in  the  general  nature  of  A,  or,  being  present,  may  be  neutral- 
ized by  some  other  element  of  A itself.  The  result  gives 
a basis  for  a probable  inference  only  ; and  the  nature  of 
that  inference  will  depend  upon  the  preponderance  of  the 
observed  happening,  or  of  the  failure  of  the  event  under 
investigation. 

The  probability  attached  to  such  an  inference,  however, 
is  different  from  the  probability  which  characterizes  the 
nature  of  enumerative  induction.  In  the  latter,  when  the 
observation  has  been  widely  extended  and  no  exceptions 


PROBABILITY 


333 


noted,  it  is  usual  to  say  the  result  expressed  in  the  propo- 
sition, Every  A is  B,  has  the  force  of  a high  degree  of 
probability.  In  the  instances,  however,  whose  investigation 
shows  the  result  that  some  H’s  are  B’s,  and  some  not,  and 
yet  where  the  former,  for  instance,  far  outnumber  the  latter 
cases,  then  it  may  be  inferred  that  the  A’s  which  in  future 
we  may  meet  with  will  probably  be  B’s ; and  the  degree  of 
probability  expressed  in  such  a proposition  is  commensurate 
with  the  preponderance  of  the  number  of  observed  affirm- 
ative instances  over  the  negative.  Here  the  probability 
refers  to  the  validity  of  an  inference  concerning  certain 
particular  instances,  be  they  many  or  be  they  few,  which 
lie  beyond  the  sphere  of  our  present  knowledge;  in  enu- 
merative  induction,  the  probability  is  attached  to  the  uni- 
versality of  the  proposition  affirmed  as  a result  of  observation 
that  has  not  so  far  detected  an  exception.  In  the  former 
case,  the  question  of  the  universality  of  the  result  is  con- 
clusively answered,  and  that  in  the  negative ; there  can  be 
no  universal  proposition  possible,  as  some  instances  give 
A and  B together,  others  give  A with  the  absence  of  _B; 
and  the  question  of  probability  that  here  arises,  therefore, 
refers  to  individual  cases  not  yet  examined,  as  to  whether 
they  severally  will  more  likely  correspond  to  the  set  of 
affirmative,  or  to  that  of  the  negative,  instances  already 
noted. 

The  comparison  of  the  number  of  happenings  with  that 
of  the  failures  of  an  event  affords  a basis  for  three  kinds  of 
inference,  all  of  them  in  the  sphere  of  probability. 

1.  We  find  in  such  a comparison  a basis  for  the  calcula- 
tion of  the  probability  of  a particular  event  happening,  in 
case  there  is  a repetition  of  the  circumstances  which,  in 
former  cases,  have  sometimes  produced  the  event,  and  some- 
times have  failed  to  produce  it.  If,  according  to  former 
observation,  the  event  has  happened,  let  us  say,  seven  times, 
and  failed  three,  the  probability,  expressed  numerically, 
of  its  happening  again  is  ^ . The  rule  is,  to  express  the 


334 


INDUCTIVE  LOGIC 


probability  of  an  event,  take  as  numerator  the  number  of 
times  which  the  event  has  been  observed  to  occur,  and  as 
denominator  the  total  number  observed,  both  of  happening 
and  failure ; the  fraction  thus  expressed  will  represent  the 
probability  of  the  event  happening.  The  counter-probability 
may  be  represented  by  the  number  of  observed  failures  of 
the  event  divided  by  the  total  number  of  cases  observed. 
The  counter-probability,  plus  the  probability,  evidently  is 
equal  to  unity.  If,  therefore,  the  probability  is  unity,  the 
counter-probability  will  equal  zero ; that  is,  the  probability 
in  that  case  has  merged  into  certainty.  Zero,  therefore, 
represents  absolute  impossibility.  All  fractions  between 
the  limits  zero  and  one  represent  varying  degrees  of  proba- 
bility from  impossibility  at  one  extreme  to  certainty  at  the 
other. 

Not  only  may  there  be  this  inductive  basis  for  the  cal- 
culation of  probability,  arising  from  actually  observed  in- 
stances; there  may  be  also  a deductive  calculation  of 
probability  based  upon  the  known  structure  or  nature  of 
the  phenomena  themselves  in  advance  of  any  observation  as 
to  their  actual  behavior.  For  instance,  we  say  the  proba- 
bility of  a penny  turning  up  heads  is  Knowing  the 
form  of  the  penny  and  that  there  are  but  two  possibilities, 
heads  or  tails,  and  there  being  no  reason  why  one  should 
more  likely  turn  up  than  the  other,  we  say  there  is  one 
chance  favorable  to  heads  as  over  against  the  two  chances 
which  represent  the  total  number  of  possibilities  under  the 
existing  circumstances.  With  a die,  in  the  form  of  a per- 
fect cube,  we  say  there  is  one  chance  of  its  turning  up  the 
face  marked  1,  as  over  against  the  six  chances  represented 
by  the  six  faces,  the  total  number ; here  the  probability  is 
4.  Thus  the  basis  for  the  calculation  of  probability  may  be 
a theoretical  as  well  as  an  empirical  one. 

In  the  estimate  of  the  probability  of  an  event  in  the 
actual  conduct  of  affairs,  we  seldom  express  that  probabil- 
ity numerically.  I would  say  that  we  express  a degree  of 


PROBABILITY 


335 


probability  adverbially  rather  than  numerically ; that  is,  we 
say  an  event  is  quite  probable,  or  it  is  very  probable,  or  it  is 
extremely  probable.  The  fact  is  that,  as  regards  most  phe- 
nomena, we  do  not  keep  an  exact  or  even  approximate  memo- 
randum of  the  number  of  happenings  compared  with  that  of 
the  failures.  We  rather  classify  our  observations  in  terms 
of  more  or  less.  For  instance,  certain  circumstances  we 
observe  produce  about  as  many  failures  as  happenings  of 
an  event;  other  circumstances  produce  far  more  happenings 
than  failures ; others  far  less,  and  so  on.  Consequently  we 
receive  certain  psychological  impressions  of  varying  degrees 
of  intensity  according  to  the  preponderance  of  happening 
over  failure,  or  vice  versa;  this  impression  becomes  the 
basis  for  estimating  the  probability  in  question,  and  the 
degree  of  that  probability  is  commensurate  with  the  inten- 
sity of  the  original  psychological  impression  arising  from 
concepts  of  more  or  of  less.  In  such  a sphere,  however,  as 
that  devoted  to  the  interests  of  betting,  gambling,  pool-sell- 
ing, book-making,  etc.,  probabilities  are  estimated  according 
to  statistical  observations  and  theoretical  considerations, 
whose  conditions  are  expressed  numerically ; and  the  amount 
risked  in  each  case  is  strictly  estimated  according  to  the 
exact  ratio  of  probability  to  counter-probability  under  the 
existing  circumstances. 

The  estimation  of  probability  in  terms  of  a greater  or 
less  degree  is  however  more  usual,  and  applicable  to  the 
conduct  of  human  life  generally.  It  has  special  force  and 
utility  as  a mode  of  inference,  when  the  observed  instances 
so  far  outnumber  the  exceptions  as  to  create  an  impression 
of  such  a high  degree  of  probability  as  to  approximate  prac- 
tical if  not  theoretical  certainty.  For  instance,  it  has  been 
noted  over  a wide  field  of  observation,  that  a second  attack 
of  scarlet  fever  is  extremely  rare.  Exceptions  have  occurred 
and  therefore  by  enumerative  induction  it  is  impossible  to 
generalize  the  universal  proposition  that  a second  attack 
will  never  occur.  It  is  however  possible  to  assert  with 


336 


INDUCTIVE  LOGIC 


somewhat  positive  assurance  that  it  is  highly  probable  that 
a person  will  be  exempt  from  a second  attack. 

Or,  yon  hear  that  a person,  whose  name  is  unknown  to 
you,  has  met  with  an  accident  in  the  city  of  New  York, 
resulting  fatally.  You  are  not  alarmed,  and  perhaps  the 
possibility  does  not  even  suggest  itself  to  you,  that  the  un- 
known person  may  prove  to  be  a member  of  your  own  family, 
or  a friend  who  at  the  time  is  known  to  be  in  New  York. 
The  probability  against  such  a suggestion  is  so  large  as  to 
preclude  even  the  thought  of  it.  Suppose,  however,  the 
accident  occurred  at  one  of  the  suburban  stations.  Your 
knowledge  that  your  friend  rides  on  one  of  the  suburban 
trains  each  day  to  and  from  town,  may  be  the  ground  of 
some  anxiety,  because  in  this  case  the  range  of  possibilities  is 
materially  narrowed.  Suppose,  moreover,  that  the  station 
where  the  accident  occurred  is  at  the  village  where  your 
friend  resides,  your  anxiety  receives  an  additional  increment ; 
and,  again,  suppose  it  is  at  the  hour  at  which  your  friend 
ordinarily  reaches  this  station,  there  is  then  increased  appre- 
hension on  his  account.  Thus,  as  further  knowledge  limits 
the  number  of  total  possible  cases,  the  denominator  of  the 
probability  fraction  is  continually  decreasing,  and  therefore 
the  probability  itself  continually  increases,  until  it  has 
developed  from  a fraction  of  insignificant  proportions  to 
one  which  is  suggestive  of  great  anxiety  and  suspense. 

2.  The  comparison  of  failure  and  happening  of  events 
based  upon  observation,  or  theoretical  considerations  of 
structure  and  nature,  leads  also  to  inferences  concerning 
large  numbers  of  instances  considered  together.  If  a 
memorandum  is  kept  of  the  number  of  times  an  event  has 
happened,  and  the  number  of  times  it  has  failed,  and  the 
total  number  of  instances  examined  be  sufficiently  great, 
then  the  resulting  ratio  of  favorable  instances  to  the  total 
number  will  be  found  approximately  repeated,  if  a second 
set  of  an  equal  number  of  instances  be  likewise  examined. 
There  is  a law  of  tendency  whereby  nature  seems  to  repeat 


PROBABILITY 


337 


herself  even  when  the  attendant  circumstances  of  an  event 
are  most  complex,  and  beyond  all  powers  of  accurate  deter- 
mination. As  the  result  of  observations  extending  over 
thousands  and  thousands  of  instances,  it  is  affirmed  that 
about  one-fourth  of  .the  children  born  in  the  world  die  be- 
fore the  age  of  six  years,  and  about  one-half  before  the  age 
of  sixteen.  Take  a group  of  ten  children,  the  ratios  would 
perhaps  be  deviated  from  very  materially ; in  a group  of  a 
hundred  the  deviation  is  apt  to  be  less;  in  a group  of  a 
thousand,  still  less ; and  in  a group  of  one  hundred  thou- 
sand, the  ratios  as  above  given  would  be  substantially  real- 
ized. The  approximation  would  be  so  near  that  the  error 
would  be  insignificant  as  compared  with  total  number  of 
cases.  The  following  law,  therefore,  expresses  this  ten- 
dency, — that  while  in  a small  number  of  instances  there  is 
irregularity  in  the  observed  ratio  between  the  number  of 
times  a given  event  has  happened  and  its  failures,  still  in  a 
large  number  of  instances  this  ratio  tends  toward  a constant 
limit.  This  is  clearly  seen  in  the  pitching  of  a penny ; 10 
throws  might  very  possibly  result  in  7 heads  and  3 tails ; 
in  100  throws,  however,  the  ratio  expressing  the  result  as 
to  heads  and  tails  observed  will  be  much  nearer  1-  than  in 
the  former  case ; while  if  1000  or  10,000  throws  be  observed, 
the  result  will  approximate  the  ratio  i.  The  comparison  of 
observed  cases  with  the  number  given  by  the  calculation  of 
the  probabilities  in  question  has  been  made  by  Quetelet, 
also  by  Jevons,  Their  results  are  most  significant  and  in- 
teresting. Quetelet  made  4096  drawings  from  an  urn  con- 
taining 20  black  balls  and  20  white.  Theoretically,  he 
should  have  drawn  as  many  white  as  black  balls,  2048  each ; 
the  actual  drawings  resulted  in  2066  white  balls  and  203C 
black.  Jevons  made  20,480  throws  of  a penny;  the  theo- 
retical result  should  have  been  10,240  heads ; the  actual 
result  was  10,353  heads. 

The  tendeucy  towards  a constant  ratio  in  aggregates  con- 
taining a considerable  number  of  instances  is  strikingly 


338 


INDUCTIVE  LOGIC 


illustrated  in  the  record  of  baptisms  taken  from  an  old  par- 
ish register  in  England.  The  number  of  male  baptisms 
registered  to  every  1000  female  ran  as  follows  for  the  re- 
spective years  from  1821  to  1830 : 1048,  1047,  1047,  1041, 
1049,  1046,  1047,  1043,  1043,  1034.  We  see  with  what  sur- 
prising accuracy  the  constant  ratio  was  repeated  substan- 
tially, year  after  year.  This  tendency  to  approximate  a 
constant  ratio  is  seen  even  in  such  indeterminate  events  as 
railroad  accidents.  Here  the  causes  producing  the  accidents 
are  so  numerous,  so  diverse,  so  complex  and  extending  over 
so  large  an  area,  — as,  for  example,  the  whole  of  the  United 
States,  — that  we  should  think  that  the  results  would  ex- 
hibit so  many  variations  from  any  definite  ratio  as  abso- 
lutely to  elude  all  attempts  at  accurate  determination.  The 
figures  on  pages  339  and  340,  however,  given  by  the  Inter- 
state Commerce  Commission,  indicate  results  wonderfully 
corresponding  for  year  after  year. 

An  examination  of  these  figures  will  disclose  the  fact  that 
there  is  a striking  approximation  to  an  accurately  propor- 
tionate distribution  of  the  number  of  accidents,  of  the  killed 
and  of  the  injured,  throughout  these  several  years.  It  will 
be  noticed,  also,  that  the  distribution  among  employees,  pas- 
sengers, other  persons,  etc.,  tends  toward  a regularity  that 
is  remarkable  when  we  consider  the  extreme  complexity  of 
the  circumstances  that  must  combine  to  produce  these  re- 
sults. A like  regularity  seems  to  pervade  every  department 
of  life.  The  total  number  of  crimes  is  approximately  the 
same,  year  after  year ; the  annual  death-rate,  the  appor- 
tionment of  deaths,  moreover,  to  the  several  diseases  as 
their  evident  causes,  the  number  of  missent  letters  that 
reach  the  Dead-Letter  Office  at  Washington  each  year,  the 
annual  number  of  suicides,  of  divorces,  all  these  diverse 
events  indicate  a regularity,  in  the  long  run,  as  regards  their 
numerical  estimate. 

The  results  which  are  thus  attained  regarding  aggregates 
cannot  be  stated  as  probable  results  merely.  If  a sufficiently 


RAILROAD  ACCIDENTS  IN  THE  UNITED  STATES 


PROBABILITY 


339 


CO  05  N H 'N  M 
CO  O CM  00  o o 
00  CO  O 00  CO  CO 


<M  CO  O O t- 

CO  W W (N 

CM  00  00  C 1— I 

O O CO  I>  I> 


' CD 

,rH  o 

O rO 

C3  ct 
bO  0! 

.2  t 

*s  ^ 

of  3 

O O 
00  .2 
G p 


iO  O CO  W O C5 
-H  H oo  05  C5 
CO  CO  <M  <M  CO  CM 


CM  ^ 


CO  Tfi  Tji  IO  o 


i— i 00  CO  t"-  o 

C5  ^ C.  N H c>l 

CO  O lO  O CM  CO 

(M  CO  CO  Tji  ^ tjc 


00  CO  O M 05 

CO  tP  CM  t-  (M  M 

i-*  r-*  tP  O CM  M 

CM  CM  CM  CM  CO  CO 


§ § 
10  S, 

1o  ^ 
O m 
*3  ^ 

03  © 

bD  CO 
c3  CO 

g ft 

^ CO 
- CD 
CO  U 

a ^ 

CO 

’"H  fl 
jh  c3 

oT 


CO  O u-  03 


CM  i— i O tP  t>- 

r—  o co  o m 

C5tPO*-OP- 
r-1  (M  <M  CM  CM 


£ 


bp 

3 

a;  CO 

£ o - 

S 1 g 

r/>  M O 


bC  05 

C co 

<D  <D 


00  C5  O H (M  CO 
00  00  O C5  C3  05 
00  00  00  00  00  00 


ct  d -P 
PU  3 O 
CO  ^ 
^ c3  - 
° O fcfi 


p 'S 
£ © 


«-■  T~ . 

n T.  p 

c3  "*v  -+-3 

3 §3  S 

o S 

rj  <D  ^ 
^ CO  © 
CS 

CD  rO 
<D  sp 


340  INDUCTIVE  LOGIC 


Average  per  year  for  five  years. 


PROBABILITY 


341 


large  number  of  instances  are  taken,  the  result  will  be  cer- 
tain within  a very  small,  and  in  many  cases  an  insignificant, 
margin.  In  estimating  the  probability  of  a single  event, 
the  question  is  whether  it  will  happen  or  not  happen,  and 
the  element  of  uncertainty  is  therefore  prominent.  In  deal- 
ing with  aggregates,  however,  no  such  element  of  uncer- 
tainty enters ; the  question  is  not  whether  or  not  there  will 
be  certain  results,  the  question  concerns  rather  the  degree 
of  exactness  with  which  the  results  will  approximate  a 
definite  ratio.  And  the  law  of  tendency  is,  that  the  larger 
the  number  of  instances,  the  greater  will  be  the  approxima- 
tion to  an  accurate  and  definite  result. 

This  is  especially  illustrated  in  the  numerous  insurance 
companies,  whose  business  is  conducted  upon  the  basis  of  an 
approximately  constant  death-rate.  For  instance,  the  gen- 
eral procedure  is  somewhat  as  follows:  Suppose  10,000 
persons  insure  their  lives  at  $1000  per  individual,  and  the 
annual  death-rate  observed  over  a rude  extent  of  territory, 
and  including  a very  large  number  of  instances,  amounts  to 
200  persons  out  of  10,000.  The  losses  then  to  the  insurance 
company  will  amount  annually  to  $200,000  on  such  a basis. 
These  losses,  distributed  among  the  10,000  insuring  in  the 
company,  would  amount  to  $20  apiece.  The  company, 
therefore,  has  a numerical  basis  for  calculating  the  amount 
which  each  person  must  pay  in  order  to  cover  the  annual 
losses  and  provide  an  assured  revenue  for  the  company. 

I have,  of  course,  stated  the  problem  in  round  numbers, 
merely  to  illustrate  in  general  the  principle  involved ; the 
actual  calculation  is  more  complicated,  because,  in  each 
particular  case,  the  age  of  the  individual  and  the  varying 
death-rates  for  different  years  must  be  taken  into  account. 
The  substantial  standing  of  the  innumerable  insurance  com- 
panies in  our  country  bears  witness  to  the  fact  that  these 
enterprises  are  based  upon  a practical  certainty  regarding 
death-rates  when  applied  to  large  aggregates.  Chance  is 
thus  eliminated  almost  entirely  ; that  which  would  be  a 


342 


inductive  logic 


serious  risk  as  regards  an  individual  is  substantially  void 
of  all  risk  when  large  numbers  are  concerned. 

Moreover,  statistics  covering  different  classes  are  often 
most  valuable  in  indicating  tendencies  operative  in  the 
classes  when  compared  one  with  another.  According  to 
M.  Loua  ( Economiste  Frangais,  1882,  Vol.  I,  p.  179),  the  fol- 
lowing are  the  figures  of  the  annual  mortality  in  Paris  : — 

The  rich  and  well-to-do  classes,  156  out  of  every  10,000  inhabitants. 
The  poor,  285  out  of  every  10,000  inhabitants. 

So  also,  in  England,  the  average  duration  of  life  among 
the  wealthy  classes  is  from  55  to  56  years  ; for  the  working 
classes  it  falls  to  28  years,  or  even  lower.1  Such  compari- 
sons are  significant  in  indicating  underlying  forces  in  society 
that  otherwise  might  be  overlooked,  or,  at  least,  not  ade- 
quately appreciated,  and  which  a limited  observation  could 
not  accurately  reveal.  Mr.  Darwin,  after  observing  and  ex- 
perimenting upon  a very  large  number  of  plants,  found  the 
following  figures  respecting  the  relative  productivity  of  cross 
and  spontaneously  self-fertilized  flowers : As  regards  the 
number  of  seeds  per  pod  yielded  by  cross  and  self-fertilized 
flowers,  the  ratio  was  100  to  41  respectively ; the  crossed 
seeds  compared  with  an  equal  number  of  the  spontaneously 
self-fertilized  seeds  were  heavier,  in  the  ratio  of  100  to  88. 2 
The  ratios  thus  disclosed  in  examining  a large  number  of 
instances  could  not  have  been  gained  by  any  experimen- 
tal method  adapted  for  dealing  with  individual  instances. 
Although  the  cause  is  not  quantitatively  determined,  a 
tendency  of  a constant  nature  toward  a definite  end  is 
clearly  indicated. 

Race  characteristics  are  often  disclosed  by  comparative 
statistics,  and  the  presence  or  absence  of  causes  possessing 
moral  significance  are  thus  revealed  which  otherwise  could 

1 Gide,  Political  Economy , p.  405. 

2 Darwin,  Cross  and  Self  Fertilization,  p.  165. 


PROBABILITY 


343 


not  be  determined  with  any  considerable  degree  of  definite- 
ness. The  following  tables  will  indicate  this  : — 

Suicides.  — In  European  cities  the  number  of  suicides  per 

100.000  inhabitants  is  as  follows : Paris,  42 ; Lyons,  29 ; 
St.  Petersburg,  7 ; Moscow,  11 ; Berlin,  36 ; Vienna,  28  ; Lon- 
don, 23  ; Pome,  8 ; Milan,  6 ; Madrid,  3 ; Genoa,  31 ; Brussels, 
15 ; Amsterdam,  14 ; Lisbon,  2 ; Christiania,  25 ; Stock- 
holm, 27 ; Constantinople,  12 ; Geneva,  11 ; Dresden,  51. 
Madrid  and  Lisbon  show  the  lowest,  Dresden  the  highest, 
figure. 

The  average  annual  suicide  rate  in  countries  of  the  world 
per  100,000  persons  living  is  given  by  Barker  as  follows : 
Saxony,  31.1 ; Denmark,  25.8  ; Schleswig-Holstein,  24.0 ; 
Austria,  21.2 ; Switzerland,  20.2 ; France,  15.7 ; German 
Empire,  14.3;  Hanover,  14.0;  Queensland,  13.5;  Prussia, 
13.3;  Victoria,  11.5;  Hew  South  Wales,  9.3;  Bavaria,  9.1 ; 
Hew  Zealand,  9.0;  South  Australia,  8.9;  Sweden,  8.1 ; Hor- 
way,  7.5  ; Belgium,  6.9  ; England  and  Wales,  6.9  ; Tasmania, 
5.3;  Hungary,  5.2 ; Scotland,  4.0;  Italy,  3.7;  Hetherlands, 
3.6 ; United  States,  3.5  ; Russia,  2.9  ; Ireland,  1.7  ; Spain,  1.4. 

The  causes  of  suicide  in  European  countries  are  reported 
as  follows  : Of  100  suicides : Madness,  delirium,  18  per  cent ; 
alcoholism,  11 ; vice,  crime,  19 ; different  diseases,  2 ; moral 
sufferings,  6 ; family  matters,  4 ; poverty,  want,  4 ; loss  of 
intellect,  14  ; consequence  of  crimes,  3 ; unknown  reasons,  19. 

Homicides.  — Italy  takes  the  lead  of  European  nations, 
with  an  average  annual  crop  of  murders  of  2470,  a ratio  per 

10.000  deaths  of  29.4 ; Spain  follows,  with  a ratio  of  23.8, 
and  1200  murders ; Austria,  ratio  of  8.8,  and  600  murders ; 
France,  ratio  of  8.0,  and  662  murders;  England,  ratio  of  7.1, 
and  377  murders.  The  figures,  however,  represent  actual 
murders,  not  homicides  from  all  causes,  as  do  those  in  the 
United  States  table. 

Illegitimacy.  — Of  each  1000  births,  the  number  illegiti- 
mate, according  to  statistics  published  in  London,  1892, 


344 


INDUCTIVE  LOGIC 


were : Russia,  27 ; Ireland,  28 ; Holland,  33  ; England  and 
Wales,  46;  Switzerland,  47;  Italy,  73;  Norway,  74;  Scot- 
land, 79;  Prussia,  80;  France,  84;  Hungary,  85 ; Belgium, 
88  ; Denmark,  93  ; Sweden,  101  ; Saxony,  125;  Bavaria,  141 ; 
Austria,  147.  No  accurate  statistics  for  the  United  States 
exist.  The  lowest  rate  in  Europe  is  that  of  Connaught,  in 
Western  Ireland,  7 per  1000.  — Dr.  Albert  Leffingwell,  Sum- 
mit, N.J. 

3.  When  phenomena  indicate  a marked  departure  from 
the  ratio  of  frequency  as  determined  by  prior  observation, 
or  by  theoretical  considerations,  then  it  is  ordinarily  inferred 
that  a new  cause  has  become  operative,  which  was  not  before 
existent,  or,  whose  effect  had  been  neutralized.  For  instance, 
we  would  naturally  expect  a die  to  show  the  face  three,  on 
an  average,  about  once  in  six  throws.  But  if  it  repeatedly 
turns  up  three  in  succession,  and  no  other  number  appears, 
or  appears  but  rarely,  we  are  warranted  in  inferring  that 
the  die  is  loaded.  The  number  of  homicides  in  the  United 
States  in  1894  far  exceeded  the  annual  number  observed  for 
the  several  years  preceding.  This  discrepancy  is  easily  ac- 
counted for  by  the  fact  that  the  natural  number  was  swollen 
by  the  deaths  caused  by  the  strikers  and  rioters  in  the 
month  of  July  of  that  year.  So  also  a marked  departure 
from  the  annual  death-rate  of  such  a city  as  New  York  is  at 
once  an  urgent  suggestion  to  the  Board  of  Health  to  start 
investigations  that  will  unearth  the  hidden  cause  that  one 
is  constrained  to  believe  must  be  present.  Such  causes  as 
defective  drains,  prevalence  of  epidemics,  etc.,  are  again 
and  again  found  to  accompany  an  increase  of  the  average 
death-rate. 

Under  such  circumstances,  the  method  of  investigation, 
when  practicable,  which  should  be  pursued,  is  to  endeavor 
to  break  up  the  total  into  smaller  groups  of  a specific  nature. 
Thus,  if  the  death-rate  for  the  year  is  appreciably  increased, 
examine  the  death-rate  per  month.  See  if  any  month  shows 


PROBABILITY 


345 


a marked  departure  from  the  average.  If  so,  this  will  sug- 
gest a careful  investigation  of  the  circumstances  and  char- 
acteristics of  the  month  in  question.  Or  it  may  be  possible 
to  make  a geographical  distribution  of  the  total  over  differ- 
ent sections  of  the  city  under  investigation.  Some  special 
locality  may  indicate  an  unusually  large  death-rate.  Inves- 
tigation, therefore,  at  that  point  may  reveal  a lurking  cause 
of  disease,  otherwise  unnoticed. 

By  similar  considerations,  also,  it  is  often  possible  to  dis- 
tinguish between  a chance  coincidence,  and  a determinate 
cause  which  may  have  produced  the  event  in  question.  For, 
if  the  possibility  of  some  one  definite  cause  is  considered  out 
of  the  question,  and  the  origin  of  the  event  is  found  among 
complex  phenomena  of  such  a number  and  variety  that  they 
may  form  an  indefinite  number  of  combinations,  only  one 
of  which  can  possibly  produce  the  event  in  question,  then 
the  probability  that  the  event  has  actually  been  produced 
by  such  a chance  combination  is  extremely  small.  We  are 
then  thrown  back  upon  the  other  hypothesis,  that,  instead 
of  one  out  of  many  possible  combinations,  there  is  some  one 
determinate  cause  operative  in  the  case.  Its  nature  may 
not  be  definitely  indicated,  but  at  least  the  possibility  of 
its  presence  is  suggested. 

This  line  of  reasoning  is  illustrated  in  the  following  ac- 
count of  the  discovery  of  the  existence  of  iron  in  the  sun, 
in  the  researches  of  Bunsen  and  Kirchhoff : “ On  comparing 
the  spectra  of  sunlight  and  of  the  light  proceeding  from  the 
incandescent  vapor  of  iron,  it  became  apparent  that  at  least 
sixty  bright  lines  in  the  spectrum  of  iron  coincided  with 
dark  lines  in  the  sun’s  spectrum.  Such  coincidences  could 
never  be  observed  with  certainty,  because,  even  if  the  lines 
only  closely  approached,  the  instrumental  imperfections  of 
the  spectroscope  would  make  them  apparently  coincident,  and 
if  one  line  came  within  half  a millimetre  of  another,  on  the 
map  of  the  spectra,  they  could  not  be  pronounced  distinct. 
Howthe  average  distance  of  the  solar  lines  on  Kirchhoff’s  map 


346 


INDUCTIVE  LOGIC 


is  two  millimetres,  and  if  we  throw  down  a line,  as  it  were 
by  pure  chance,  on  such  a map,  the  probability  is  about  i 
that  the  new  line  will  fall  within  one-half  millimetre  on 
one  side  or  the  other  of  some  one  of  the  solar  lines.  To 
put  it  in  another  way,  we  may  suppose  that  each  solar  line, 
either  on  account  of  its  real  breadth,  or  the  defects  of  the 
instrument,  possesses  a breadth  of  one-half  millimetre,  and 
that  each  line  in  the  iron  spectrum  has  a like  breadth.  The 
probability,  then,  is  just  \ that  the  centre  of  each  iron  line 
will  come  by  chance  within  one  millimetre  of  the  centre  of 
a solar  line,  so  as  to  appear  to  coincide  with  it.  The  prob- 
ability of  casual  coincidence  of  each  iron  line  with  a solar 
line  is  in  like  manner  i.  Coincidence  in  the  case  of  each 
of  the  sixty  iron  lines  is  a very  unlikely  event  if  it  arises 
casually,  for  it  would  have  a probability  of  only  (^j60  or 
less  than  one  in  a trillion.  The  odds,  in  short,  are  more 
than  a million  million  millions  to  unity  against  such  a cas- 
ual coincidence.  But  on  the  other  hypothesis,  that  iron 
exists  in  the  sun,  it  is  highly  probable  that  such  coincidences 
would  be  observed;  it  is  immensely  more  probable  that  sixty 
coincidences  would  be  observed  if  irop  existed  in  the  sun, 
than  that  they  should  arise  from  chance.  Hence,  by  our 
principle,  it  is  immensely  probable  that  iron  does  exist  in 
the  sun.”  1 

This  principle  is  also  illustrated  in  instances  of  circum- 
stantial evidence.  In  such  cases,  the  observed  combination 
of  so  many  diverse  circumstances,  even  as  regards  an  indefi- 
nite number  of  minor  details,  precludes  the  hypothesis  of 
casual  coincidence,  and  suggests  some  one  definite  cause 
that  will  prove  a unifying  principle  of  explanation  of  all 
the  attendant  circumstances.  As  Mr.  Justice  Bullen  says: 
“ A presumption  which  necessarily  arises  from  circum- 
stances is  very  often  more  convincing  and  more  satisfactory 
than  any  other  kind  of  evidence.  It  is  not  within  the 
reach  and  compass  of  human  abilities  to  invent  a train  of 
1 Jevons,  Principles  of  Science,  pp.  244,  245. 


PROBABILITY 


347 


circumstances  which  shall  be  so  connected  together  as  to 
amount  to  a proof  of  guilt  without  affording  opportunities 
to  contradict  a great  part,  if  not  all,  of  these  circumstances.” 

The  following  account,  taken  from  The  New  York  Law 
Journal,  illustrates  the  probative  force  of  circumstantial 
evidence : — 

In  Nicholas  v.  Commonwealth  (March  1895,  21  S.  E.  R.  364)  the 
Supreme  Court  of  Appeals  of  Virginia  sustained  a conviction  of  mur- 
der, the  criminal  agency  being  established  by  circumstantial  evidence. 
The  following  extract  from  the  opinion  presents  the  main  facts  which 
implicated  the  defendant : — 

“ On  the  8th  day  of  December,  1892,  Philip  Norman  Nicholas,  the 
plaintiff  in  error,  one  James  Mills,  and  his  wife,  Anna  A.  Mills,  and 
their  three  small  children,  were  living  in  the  upper  part  of  Henrico 
County,  on  a farm  known  as  the  ‘ Wickham  Place,’  about  one  mile 
from  James  River.  Nicholas  was  the  renter  of  this  farm,  and  culti- 
vated it  on  shares.  He  was  himself,  however,  chiefly  engaged  as  a 
trapper,  having  a number  of  traps  set  along  both  sides  of  the  river. 
He  employed  James  Mills,  with  whom  he  lived,  and  one  William  Jud- 
son  Wilkerson,  as  sub-tenants,  to  do  the  farm  work,  for  a portion  of 
his  share  of  the  crops.  Wilkerson  lived  with  an  aged  mother  in  a 
small  house  very  near  to  Mills’s  house  — near  enough  to  see  into  the 
windows  of  one  house  from  the  other.  Philip  N.  Nicholas,  the  pris- 
oner, was  an  unmarried  man,  and  lived  in  a room  of  the  house  occu- 
pied by  James  Mills  and  his  family.  The  evidence  shows  that  on  the 
night  before  the  drowning,  the  prisoner,  James  Mills,  and  William  J. 
Wilkerson  were  together  at  the  house  of  Mrs.  Wilkerson,  the  latter’s 
mother,  and  there  arranged  and  determined  upon  a trip  across  the 
river  the  next  morning,  to  take  a bee  tree.  This  expedition  was  sug- 
gested, planned,  and  carried  out  by  the  prisoner.  Wilkerson  was  very 
unwilling  to  go,  and  finally  consented  at  the  suggestion  of  his  mother, 
who  said  that,  as  Mr.  Nicholas  seemed  so  anxious  for  him  to  go,  he 
had  better  do  so.  Mills  was  unwilling  to  go  unless  Wilkerson  went. 
Wilkerson  said  he  would  rather  plough  than  go.  The  prisoner  replied, 
‘ If  you  will  go,  you  shall  not  lose  anything.’  In  the  course  of  con- 
versation which  resulted  in  this  expedition  being  agreed  upon,  both 
Mills  and  Wilkerson  stated,  in  the  presence  of  Nicholas,  that  they 
could  not  swim,  and  were  very  much  afraid  of  water  ; that  they  did 
not  like  water  more  than  knee-deep.  The  fact  that  they  could  not 
swim  was  generally  known  to  their  friends.  It  is  further  shown  that 


348 


INDUCTIVE  LOGIC 


it  was  the  habit  of  Nicholas  to  go  every  morning,  early,  to  the  river, 
to  examine  his  traps.  And  it  appears  from  the  evidence  that  on  the 
morning  of  the  day  the  drowning  occurred  he  went  to  the  river  about 
daylight,  and  returned  about  breakfast  time,  and,  when  questioned 
about  it,  said:  ‘ I did  not  go  to  my  traps  this  morning.  I was  sick.’ 
He  afterwards  told  Mrs.  Wilkerson  he  did  not  catch  anything. 
Everything  being  in  readiness  to  carry  out  the  plan  for  the  day, 
these  three  men  started  from  home  about  nine  o’clock  in  the  morning, 
equipped  with  everything  necessary  for  taking  the  bee  tree ; having 
with  them  two  buckets  holding  two  and  one-half  to  three  gallons  each  for 
the  honey,  two  axes,  one  hatchet,  and  a piece  of  netting  to  protect  the 
person  from  the  bees.  The  boat  used  belonged  to  one  Joseph  Bruin, 
and  on  their  way  to  the  river  an  uncle  of  the  owner  was  asked  if  they 
might  use  the  boat,  and  was  told  they  could  get  the  key  which  un- 
locked the  boat  from  its  fastening  to  the  bank  from  Bruin,  the  owner. 
The  prisoner  replied  that  he  had  a key  of  his  own,  and  had  often  used 
it  before  without  permission.  It  appears  that  they  landed  on  the 
Chesterfield  side  of  the  river,  at  a point  one  mile  and  a half  from 
where  any  one  lived,  and  proceeded  to  the  bee  tree,  which  was  one 
mile  from  the  point  of  landing.  Investigation  showed  that  there  were 
no  tracks  about  the  point  of  landing  but  those  of  the  three  men  going 
from  and  returning  to  the  boat.  It  further  appears  from  the  state- 
ment of  the  prisoner  that  after  reaching  the  tree  they  concluded  not 
to  cut  it,  because  it  was  a large  tree,  near  the  main  road,  and  might 
get  them  into  trouble,  and  for  the  farther  reason  that  the  hole  was 
small,  and  it  might  not  have  any  honey  in  it  anyhow.  The  tree  was 
afterwards  cut  by  order  of  the  Magistrate  and  found  to  be  full  of 
honey.  It  further  appears  that  the  boat  was  a small  one,  about  ten 
feet  long  and  about  two  and  one-half  feet  wide,  and  that  both  in  going 
over  and  returning  the  prisoner  sat  in  the  extreme  rear  of  the  boat, 
with  his  face  to  the  front,  and  that  Wilkerson  and  Mills  sat  in  front 
of  him,  with  their  faces  to  the  front  and  their  backs  to  the  accused. 
This  position  of  the  parties  the  prisoner  admitted  very  reluctantly, 
when  questioned  about  it.  When  returning,  and  about  fifty  yards 
from  the  Henrico  shore,  the  boat  suddenly  filled  with  water,  and  Mills 
and  Wilkerson  were  drowned,  and  the  prisoner  swam  to  shore.  The 
next  day  the  Magistrate  of  the  district  was  notified  of  the  occurrence, 
and  an  investigation  was  set  on  foot.  The  boat  was  gotten  out  of  the 
water,  and  it  was  found  that  immediately  under  the  seat  where 
Nicholas  sat  there  were  three  holes,  freshly  bored  with  an  inch  and  a 
half  auger.  The  evidence  of  the  owner  of  the  boat  shows  that  on 
Tuesday  evening,  the  6th  of  December,  he  used  his  boat,  and  it  was 


PROBABILITY 


349 


sound.  It  was  taken  by  Nicholas  for  this  fatal  trip  Thursday  morn- 
ing, the  8th  of  December.  Further  investigation  discovered  fresh  pine 
shavings  corresponding  to  size  of  the  holes  and  to  the  wood  the  boat 
was  made  of,  which  had  been  thrown  into  the  water,  but  had  drifted 
upon  the  shore  near  the  point  where  the  boat  had  stood  fastened  to 
the  Henrico  side.  There  were  also  found  corn-cobs  which  had  been 
cut  to  exactly  fit  the  holes  in  the  boat,  which  had  also  drifted  to  the 
same  point.  It  was  shown  that  the  prisoner  had  in  his  possession  an 
auger  just  the  size  of  the  holes.  This  the  prisoner  at  first  denied,  but 
afterwards  said  that  it  must  be  about  the  place  somewhere.  Diligent 
search  was  made  for  the  auger,  but  it  was  never  found. 

“ Taken  together,  the  case  is  an  interesting  illustration  of  the  con- 
clusive probative  force  of  circumstantial  evidence,  provided  there  is 
enough  of  it.  The  old  saying  that  ‘ murder  will  out  ’ is  almost  unex- 
ceptional^ true  as  to  murders  of  elaborate  stealth  and  complexity  of 
detail.  Once  let  a clue  be  obtained  to  the  chain  of  causation  and 
motive,  and  the  mystery  unravels  almost  of  itself.  It  is  quite  natural 
that  most  of  the  elaborately  planned  murders  of  recent  times  should 
have  been  by  poison.  And  the  Harris,  Buchanan,  and  Meyer  cases 
in  New  York  disclose  how  comparatively  easy  detection  and  convic- 
tion are  in  crimes  of  such  class.  It  is  significant  that  two  of  the  great- 
est enigmas  in  American  criminal  annals  during  the  last  quarter  of  a 
century  have  been  the  Nathan  murder  and  the  Borden  murder.  In 
both  cases  the  killing  was  done  not  by  methods  calculated  to  conceal 
the  agency  of  a murderer,  but  in  the  most  primitive  and  brutal  man- 
ner. No  traceable  physical  clue  to  any  particular  person  was  left,  and 
we  are  inclined  to  believe  that  in  both  cases  the  connection  of  the  mur- 
derer with  the  crime  was  merely  casual  or  accidental.”  1 

In  the  various  illustrations  which  have  been  given  we  find 
that  the  theory  of  probability  provides  a method  of  dealing 
with  phenomena  which  cannot  be  subjected  to  the  ordinary 
inductive  methods.  The  phenomena  are  so  complex  that  a 
specific  cause  cannot  be  determined,  for  the  real  cause  in 
question  is  a correlation  of  many  diverse  forces,  and  if  only 
a few  instances  are  examined  no  causal  connection  will  be 
disclosed;  it  is  necessary,  therefore,  to  deal  with  large 
numbers,  statistical  averages,  etc.,  in  order  to  detect  an 
emerging  relation  of  a causal  character,  expressed  by  a 

1 The  New  York  Law  Journal,  Thursday,  May  2,  189o. 


350 


INDUCTIVE  LOGIC 


constant  ratio.  This  ratio  once  determined,  it  becomes  a 
further  test,  as  we  have  already  seen,  when  the  results 
widely  depart  from  it,  to  suggest  the  presence  of  a new 
force  outside  of  the  combinations  to  which  the  effect  would 
be  naturally  referred  according  to  the  indications  of  the 
probability-ratio.  This  latter  mode  of  inference  is  akin  to 
the  method  of  residues,  for  the  inference  in  question  is 
based  upon  the  fact  that  the  probability-ratio  will  account 
for  only  a certain  frequency  of  occurrence  of  the  event 
under  investigation ; a marked  excess  must  be  accounted 
for  by  positing  a definitely  operative  cause.  And  if  an 
antecedent  of  such  a nature  is  known  to  be  present,  the 
suggestion  at  once  rises  in  our  thought  that  this  in  all 
probability  is  the  cause  producing  this  excess  in  the  results. 


CHAPTER  XV 


EMPIRICAL  LAWS 

There  is  a class  of  laws  which  are  intermediate  between 
a universal,  inductively  grounded  by  scientific  determina- 
tion, and  a law  of  tendency  which  expresses  the  probability 
of  the  happening  of  an  event  in  spite  of  recognized  excep- 
tions. These  are  laws  which  have  been  observed  to  obtain 
under  given  conditions  of  time,  place,  and  circumstance,  and 
yet  the  causal  relation  not  sufficiently  determined  to  warrant 
a necessary  extension  of  the  same  to  a sphere  beyond  that 
wherein  it  has  been  observed  to  be  operative.  Such  laws 
are  known  as  Empirical  Laws. 

We  have  three  classes  of  laws  possessing  varying  degrees 
of  probability.  (1)  The  first  is  where  there  has  been  a 
scientifically  determined  causal  connection  between  ante- 
cedent and  consequent;  and  not  only  have  no  exceptions 
been  noted,  but  the  possibility  of  there  being  an  excep- 
tion has  been  eliminated  by  strict  experimental  methods. 
(2)  The  second  is  where  the  regularity  of  sequence  has 
been  broken  by  actual  exceptions,  and  the  result  of  the 
observations  of  instances  gives  an  indication  only  of  the 
relative  frequency  of  occurrence  and  failure  which  will 
probably  characterize  other  events  of  that  nature.  (3)  The 
third  class  and,  as  has  been  said,  an  intermediate  class, 
comprises  all  expressions  of  uniform  sequence  or  coexist- 
ence, where  no  exception  whatsoever  has  been  rioted,  and 
yet  there  is  no  ground  for  necessitating  a universal  expres- 
sion of  the  observed  uniformity.  There  is  here  always  a 
possibility  of  an  exception  appearing,  or  of  an  exception 

351 


352 


INDUCTIVE  LOGIC 


having  been  overlooked.  This  produces  an  element  of  un- 
certainty which  pervades  all  phenomena  of  this  sort. 

There  are  several  kinds  of  empirical  laws,  as  follows:  — 

1.  Where  the  causal  relation  is  in  process  of  scientific 
determination ; a uniform  connection  between  phenomena 
has  been  observed,  and  as  yet  has  not  been  proved.  All 
laws,  finally  determined  as  expressions  of  causal  connec- 
tion, pass  through  this  empirical  stage.  Some  expressions 
of  uniform  relations  never  pass  beyond  this  stage,  be- 
cause, as  we  have  seen,  the  nature  of  the  phenomena  may 
be  such  as  to  preclude  all  experiment  or  even  indirect 
verification. 

Empirical  laws  may  become  ultimate  laws  or  derivative 
laws,  as  the  case  may  be.  Ultimate  laws  are  those  wherein 
the  causal  relation  between  a simple  antecedent  and  its 
corresponding  consequent  has  been  scientifically  determined 
in  terms  of  their  exact  quantitative  variation,  and  expressed 
in  the  simplest  form  possible.  The  derivative  laws  how- 
ever as  the  name  indicates,  are  more  concrete  expressions 
of  the  ultimate  and  simpler  laws  to  which  they  are  referred 
as  special  cases.  An  empirical  law  may  be  proved  directly 
an  ultimate  law,  or  be  proved  a derivative  law  directly 
traceable  to  an  ultimate  law,  as  its  basis,  or  logical  ground. 
We  may  observe  that  a glass  of  ice-water  always  shows 
drops  of  moisture  on  its  outer  surface.  This  uniformity  as 
thus  expressed  has  the  force  only  of  an  empirical  law.  No 
attempt  having  been  made,  as  yet,  to  explain  the  presence 
of  the  moisture,  its  empirical  nature  is  evident.  But  as 
soon  as  the  moisture  on  the  glass  is  traced  to  the  condensa- 
tion of  the  moisture  in  the  atmosphere  owing  to  the  differ- 
ence of  temperature  between  the  atmosphere  and  the  cold 
surface  of  the  glass,  we  have  the  empirical  law  becoming 
a derivative  law;  that  is,  the  expression  of  a uniform 
sequence  directly  traceable  to  the  more  ultimate  laws  of  the 
saturation  and  condensation  of  vapors.  The  progress  of 
scientific  and  logically  accurate  thought  is  always  marked, 


EMPIRICAL  LAWS 


353 


therefore,  by  the  resolution  of  empirical  generalities  into 
derivative  or  ultimate  laws. 

2.  The  character  of  an  empirical  law  is  attached  to  the 
relation  existing  between  antecedent  and  consequent,  when 
that  relation  is  a complex  one  in  which  a simple  causal 
relation  is  so  involved  with  other  elements  entering  into 
combination  with  it,  that  its  real  nature  is  thus  hidden  and 
cannot  readily  be  disclosed.  This  class  includes  all  causal 
relations  due  to  collocations  of  various  kinds  that  are  neces- 
sary to  produce  the  required  effect.  As  Mill  has  pointed 
out : “ It  is  the  nature  of  an  empirical  law  that  we  do  not 
know  whether  it  results  from  the  different  effects  of  one 
cause  or  the  effects  of  different  causes.  We  cannot  tell 
whether  it  depends  wholly  upon  laws,  or  partly  upon  laws 
and  partly  upon  a collocation.  If  it  depends  upon  a colloca- 
tion, it  will  be  true  in  all  the  cases  in  which  that  particular 
collocation  exists.  But  since  we  are  entirely  ignorant,  in 
case  of  its  depending  upon  a collocation,  what  the  colloca- 
tion is,  we  are  not  safe  in  extending  the  law  beyond  the 
limits  of  time  and  place  in  which  we  have  actual  experience 
of  its  truth.  Knowing  of  no  rule  or  principle  to  which  the 
collocations  themselves  conform,  we  cannot  conclude  that 
because  a collocation  is  proved  to  exist  within  certain  limits 
of  place  or  time,  it  will  exist  beyond  those  limits.”  1 

There  are  many  illustrations  of  such  observed  generalities 
where  the  effect  is  due  largely,  if  not  altogether,  to  colloca- 
tions. The  effect  of  certain  medicines  upon  the  human  sys- 
tem, the  opening  and  shutting  of  some  flowers  at  certain 
hours  of  the  day,  the  local  action  of  tides  at  various  places 
on  the  earth’s  surface,  the  adaptation  of  certain  plants  to  a 
peculiar  kind  of  soil,  the  reappearance  of  some  chronic  dis- 
eases, as  hay-fever,  at  the  same  season  each  year,  even  to  the 
very  day  of  the  month,  — all  such  generalities  have  merely 
an  empirical  weight,  and  the  effects  mentioned  are  largely 
due  to  collocations  that  cannot  be  definitely  determined.  So 
i Mill,  Logic,  Book  III,  Chap.  XVI,  § 4. 


354 


INDUCTIVE  LOGIC 


also  certain  laws  or  customs  may  have  proved  beneficial  in 
the  countries  in  which  they  have  been  tried,  and  yet,  in 
countries  where  condition  and  circumstance  are  radically 
different,  they  may  fail  wholly  of  beneficial  results. 
There  may  be  also  certain  industrial  circumstances  which 
in  one  country  might  be  conducive  to  prosperity,  and 
in  another  country  to  adversity.  Certain  agricultural 
methods  which  in  one  section  of  the  country  tend  to  an 
increase  of  productive  power,  in  another  might  prove  a 
complete  failure.  A governmental  policy  may  in  one  coun- 
try lead  to  unparalleled  success  ; in  another,  however,  a like 
policy  might  lead  to  disastrous  results. 

The  famous  formula  of  Malthus,  that  population  tends  to 
increase  in  a geometrical  progression,  whilst  the  means  of 
subsistence  can  only  increase  in  an  arithmetical  progression, 
can  have  only  an  empirical  force.  Its  extension  into  an 
indefinite  future  is  unwarrantable.  As  is  known,  produc- 
tion has  increased  enormously  and  at  a ratio  vastly  greater 
than  any  contemplated  by  Malthus  as  at  all  in  the  range 
of  possibility.  Many  causes,  on  the  other  hand,  may  com- 
bine to  check  the  rapid  increase  of  population.  The  colloca- 
tions here  are  so  complex  as  to  defy  any  definite  prediction. 
This  is  true  of  all  tendencies  which  are  due  to  present  social 
conditions ; the  conditions  themselves  may  so  vary  in  time 
to  come  as  to  change  totally  the  accepted  generalizations  of 
to-day.  Their  empirical  character  is  therefore  most  evi- 
dent. 

3.  A third  class  of  empirical  laws  comprises  all  those 
generalizations  which  represent  a correlation  of  properties 
in  the  same  individual.  In  all  such  cases  no  causal  relation 
has  been  specifically  determined  between  the  properties 
themselves,  or  between  the  properties  and  the  whole  in 
which  they  coinhere.  Outside  of  our  experience,  the  prop- 
erties observed  might  be  materially  changed,  and  yet  not 
affect  the  integrity  of  the  concept  in  general.  A propo- 
sition such  as,  All  swans  are  white,  can  have  only  empirical 


EMPIRICAL  LAWS 


355 


force;  for  beyond  our  experience,  tbe  discovery  of  black 
swans  would  forbid  the  proposition  being  regarded  in  the 
light  of  a universal.  Many  properties  of  substances  are 
thus  referred  to  the  nature  of  the  substance  itself  as  their 
ground,  and  yet  because  the  exact  causal  relation  is  not 
determined,  the  connection  can  be  considered  only  as  an 
empirical  one.  In  other  words,  reference  to  some  ground 
as  explanation  of  a phenomenon,  without  explaining  why 
or  how  such  reference  is  made,  has  always  the  force  of  an 
empirical  law  only.  The  following  are  empirical  gen- 
eralizations of  this  nature : Copper  is  ductile ; steel  is 
elastic;  glass  is  brittle  and  transparent;  the  compound  sili- 
cates of  alkalies  and  alkaline  metals  are  transparent ; and 
other  instances  of  like  nature  that  can  be  multiplied  indefi- 
nitely. 

In  the  sphere  of  biology,  Mr.  Spencer  has  drawn  attention 
to  the  fact  that  “during  the  era  in  which  uniformity  of 
many  quite  simple  inorganic  relations  was  still  unrecog- 
nized, certain  organic  relations,  intrinsically  very  complex 
and  special,  were  generalized.  The  constant  coexistence  of 
feathers  and  a beak,  of  four  legs  with  an  internal  bony 
framework,  are  facts  which  were,  and  are,  familiar  to  every 
savage.  Did  a savage  find  a bird  with  teeth,  or  a mammal 
clothed  with  feathers,  he  would  be  as  much  surprised  as  an 
instructed  naturalist.  Now  these  uniformities  of  organic 
structure,  thus  early  perceived,  are  of  exactly  the  same 
kind  as  those  more  numerous  ones  later  established  by 
biology.  The  constant  coexistence  of  mammary  glands 
with  two  occipital  condyles  to  the  skull,  of  vertebrae  with 
teeth  lodged  in  sockets,  of  frontal  horns  with  the  habit 
of  rumination,  are  generalizations  as  purely  empirical  as 
those  known  to  the  original  hunter.  The  botanist  cannot 
in  the  least  understand  the  complex  relation  between 
papilionaceous  flowers  and  seeds  borne  in  flattened  pods ; 
he  knows  these  and  like  connections  simply  in  the  same 
way  that  the  barbarian  knows  the  connections  between 


356 


INDUCTIVE  LOGIC 


particular  leaves  and  particular  kinds  of  wood.”1  Such 
knowledge  as  Mr.  Spencer  here  describes  is  a knowledge  of 
the  coexistence  of  two  phenomena  in  their  totality  which 
resist  all  attempts  to  analyze  into  their  component  parts. 
Moreover,  laws  which  are  but  general  descriptions  of 
correlated  events  have  the  same  force  as  the  descriptions 
of  coinhering  attributes  of  substances.  They,  too,  rank 
as  empirical  generalizations.  The  successive  stages  in 
the  growth  of  a plant  from  seed  to  flower  and  fruit, 
the  embryonic  as  well  as  the  post-natal  developments 
in  animal  life,  the  habits  and  instincts  of  animals,  — all 
these  are  descriptive  generalizations  without  any  attempt 
at  causal  determination. 

4.  All  generalizations  expressed  in  terms  of  probability 
only,  because  of  known  exceptions,  rank  as  empirical  laws. 
Here,  even  in  the  time,  place,  and  circumstance  of  observa- 
tion, the  law  has  not  been  found  always  valid.  The  signifi- 
cance of  an  empirical  law,  if  we  allow  this  latter  class  to 
be  included  under  them,  is  evidently  that  of  the  contra- 
dictory of  a law  which  is  the  result  of  a causal  determina- 
tion. Every  generalization  not  causally  determined  is  then 
to  be  regarded  as  an  empirical  law.  There  is,  however,  a 
narrower  usage  of  the  term  which  does  not  include  this 
latter  class ; namely,  a restriction  of  the  term  empirical 
law  to  signify  the  expression  of  a relation  which  has  been 
found  constant  throughout  the  sphere  of  observation,  and 
yet  where  there  exists  no  known  causal  ground  by  reason 
of  which  we  would  be  warranted  in  inferring  the  continua- 
tion of  this  relation  in  a sphere  beyond  that  already  observed. 
We  might  add  that  with  this  there  is  also  the  expecta- 
tion, greater  or  less,  according  to  the  circumstances  attend- 
ing the  phenomena,  that  the  generalized  experience  will  be 
further  confirmed  by  subsequent  observation  in  a wider 
sphere.  This  restricted  meaning  of  an  empirical  law  is 
the  one  generally  understood,  unless  it  is  implied  to  the 
contrary. 

1 Spencer,  Classification  of  the  Sciences,  p.  53. 


EMPIRICAL  LAWS 


357 


An  empirical  uniformity  generally  results  from  the  method 
of  agreement.  Observed  instances,  even  so  selected  as  to 
vary  the  antecedents  as  much  as  possible,  cannot  alone 
establish  a law  of  uniformity  that  shall  have  universal 
validity.  The  method  of  agreement,  we  have  seen,  needed 
to  be  supplemented  by  the  method  of  difference  if  possible, 
or  by  an  hypothesis  capable  of  subsequent  verification.  An 
empirical  law  is,  therefore,  due  either  to  some  deficiency  in 
method,  or  to  the  natural  limitations  of  our  knowledge. 

The  element  of  uncertainty  attached  to  all  inferences 
depending  upon  the  extension  of  an  empirical  law  into  un- 
known territory,  it  has  been  insisted  upon,  may  apply  equally 
as  well  to  all  inferences  depending  upon  the  results  of  the 
inductive  methods  even  when  most  scientifically  determined. 
It  is  contended  that  even  a causal  relation,  however  firmly 
grounded,  and  however  simple  may  be  its  nature,  neverthe- 
less presents  an  empirical  character.  It  may  give  assurances 
of  a high  degree  of  probability,  but  can  never  produce  abso- 
lute certitude  in  our  minds.  Mr.  Venn,  for  instance,  has 
styled  his  work  on  induction,  Empirical  Logic,  that  by  the 
title  he  might  indicate  his  point  of  view  in  this  regard.  He 
says  in  the  preface  to  his  work : “ By  the  introduction  of 
the  term  empirical  into  the  title,  I wish  to  emphasize  my 
belief  that  no  ultimate  objective  certainty,  such  as  Mill,  for 
instance,  seemed  to  attribute  to  the  results  of  induction,  is 
attainable  by  any  exercise  of  the  human  reason.”  Regarded 
in  this  light,  all  laws  are  empirical. 

The  distinction,  however,  between  empirical  laws  in  the 
sense  generally  understood,  and  laws  expressing  causal  rela- 
tions scientifically  determined,  is  a real  distinction,  and  a 
significant  one  as  well.  And  this  must  not  be  overlooked ; 
and  it  cannot  be  obliterated  by  any  shifting  of  the  point 
of  view.  Bor,  to  doubt  the  validity  of  an  empirical  law 
when  extended  to  a sphere  beyond  that  which  has  been 
observed,  casts  a reflection  merely  upon  one’s  ability  ade- 
quately to  determine  the  connections  existing  between  the 


358 


INDUCTIVE  LOGIC 


various  elements  involved  in  the  particular  phenomena  under 
investigation.  This  is,  however,  no  confession  of  inability 
to  discover  the  causal  connections  of  phenomena  in  general, 
in  such  a manner  as  to  determine  laws  of  universal  validity. 
To  say  that  all  laws  have  only  empirical  significance  is  to 
reflect  upon  the  basal  postulates  of  knowledge.  Our  world 
is  the  world  as  we  know  it,  the  world  of  our  consciousness. 
To  discredit  the  uniformities  and  regularities  therein  exist- 
ing, and  which  find  expression  in  universal  laws,  is  to  dis- 
credit that  which  we  feel  obliged  to  think  in  order  that  our 
world  of  knowledge  regarded  as  a system  may  remain  con- 
sistent with  itself,  part  to  part,  and  part  to  whole.  We 
must,  therefore,  regard  an  empirical  law  not  as  the  final 
form  of  knowledge,  or  the  goal  of  inductive  research,  but 
rather  as  marking  a transition  stage  toward  complete  causal 
determination.  And  even  when,  owing  to  the  nature  of 
certain  phenomena,  we  are  not  able  to  pass  beyond  this 
transition  stage  of  empirical  determination,  nevertheless, 
such  instances  by  contrast  bear  unimpeachable  testimony  to 
the  fact  that  there  are  other  phenomena  of  such  a nature 
that  it  is  possible  to  subject  them  to  an  analysis  which  will 
disclose  causal  connections  of  such  a character  as  to  form  a 
basis  for  the  formulation  of  universal  laws. 


CHAPTER  XVI 


INDUCTIVE  FALLACIES 

A consideration  of  the  various  kinds  of  inductive  fal- 
lacies, and  their  characteristic  features,  may  be  regarded  as 
the  obverse  representation  of  the  general  theory  of  induc- 
tion. From  the  one  point  of  view  we  consider  the  positive 
conditions  of  true  inductive  inference ; from  the  obverse 
point  of  view  we  regard  the  various  breaches  of  these  in- 
ductive conditions.  The  discussion  of  fallacies,  therefore, 
indicates  no  progress  in  the  elucidation  of  the  subject  under 
consideration  ; it  rather  serves  to  emphasize  distinctions  and 
requirements  already  indicated  by  presenting  them  in  a new 
light,  and  from  a different  angle.  The  subject  of  fallacies 
is  generally  treated  by  exhibiting  through  various  illustra- 
tions the  cases  in  which  the  positive  conditions  of  inductive 
inference  have  failed  of  satisfactory  fulfilment.  Such  illus- 
trations of  the  infringement  of  the  requirements  of  valid 
induction,  I have  endeavored  to  incorporate  in  the  body  of 
the  text  in  connection  with  the  exposition  of  the  various  con- 
ditions and  requirements  themselves.  In  this  chapter  I shall 
attempt  to  indicate  those  fallacies  especially  which  are  due  to 
the  psychological  disturbance  of  our  normal  logical  processes. 
An  enumeration  of  these  tendencies,  partly  psychological 
and  partly  logical,  may  serve  to  impress  upon  us  the  danger 
of  falling  into  easy  errors,  to  which  the  human  mind  gen- 
erally is  liable.  These  errors  emerge  in  the  various  mental 
processes.  They  are  as  follows  : — 

I.  Errors  of  Perception. 

II.  Errors  of  Judgment. 

III.  Errors  of  the  Imagination. 

IV.  Errors  of  the  Conceptual  Processes. 

359 


360 


INDUCTIVE  LOGIC 


I.  Errors  of  Perception.  — Observation  is  the  instrument 
of  research  preeminently,  in  all  inductive  inquiry.  Experi- 
ment is  but  a method  for  increased  facility  and  accuracy  of 
observation.  We  may  say  therefore  that  all  the  data  of 
inductive  inference  are  furnished  by  this  one  process,  ob- 
servation. Any  derangement  of  our  powers  of  observation 
will  affect  the  nature  of  the  data,  and  therefore  the  nature 
of  the  results  of  induction.  It  becomes  therefore  all 
important  that  we  should  be  appraised  at  least  of  the 
various  circumstances  whose  tendency  it  is  to  operate  in  the 
midst  of  the  perceptive  processes  as  disturbing  forces.  We 
have  the  following  possibilities  of  error  in  the  sphere  of 
perception : — 

1.  Errors  due  to  a failure  to  take  in  the  whole  field  of 
vision.  There  may  be  portions  omitted  which  possess  a 
determining  significance  as  regards  the  object  of  investiga- 
tion. Thus  exceptions  may  be  overlooked  that  might  have 
an  important  bearing  upon  some  received  hypothesis;  ora 
fact  might  be  passed  by  which,  if  known,  would  prove 
highly  suggestive.  Various  devices  have  been  employed  to 
enlarge  the  sphere  of  observation  beyond  the  natural  limits 
of  the  senses.  As,  for  instance,  sounds  which  are  inaudible 
to  us  may  be  detected  by  means  of  a sensitive  flame ; the 
telescope,  the  microscope,  serve  to  render  the  distant  near, 
and  the  small  large.  It  had  been  noted  that  there  was  a 
sudden  elongation  of  an  iron  wire  at  a particular  tempera- 
ture whilst  under  longitudinal  strain  during  the  act  of 
cooling  from  a red  heat ; an  additional  circumstance  was 
noted  by  Professor  Barrett  when  performing  the  experiment 
in  a darkened  room,  namely,  that  at  the  moment  of  elonga- 
tion the  wire  suddenly  evolved  heat,  and  exhibited  a visible 
and  conspicuous  momentary  glow  of  redness.1  This  circum- 
stance it  would  be  impossible  to  note  unless  in  a darkened 
room.  Thus,  a prominent  characteristic  of  scientific  obser- 
vation is  the  endeavor  to  extend  continually  the  sphere  of 
1 Gore,  The  Art  of  Scientific  Discovery,  p.  321. 


INDUCTIVE  FALLACIES 


361 


observation.  Here  also  much  depends  upon  the  mental 
habit.  There  are  some  who  naturally  see  wider  and  farther 
than  others.  And  it  is  absolutely  necessary  that  the  true 
observer  should  cultivate  with  all  assiduity  such  a habit 
vrhen  it  is  not  a natural  possession.  There  is  a slovenliness 
in  observation  which  gives  to  the  inferences  based  upon  its 
results  a color  of  indefiniteness  and  inaccuracy,  and  which 
proves  a fertile  source  of  error. 

It  also  often  happens,  that,  owing  to  the  mind  being 
prepossessed  by  a certain  idea  or  theory,  research  will  be 
thereby  restricted  to  a limited  region,  and  neighboring 
regions  be  wholly  overlooked.  An  open-eyed  vision,  in 
spite  of  all  preconceptions  or  prejudices,  is  the  prime 
requisite  for  securing  from  all  quarters  the  greatest  possible 
array  of  facts  that  may  in  any  way  tend  to  the  formation 
of  a clearer  and  more  adequate  judgment. 

2.  A second  error  of  observation  arises  from  an  opposite 
mental  habit,  a failure  properly  to  concentrate  the  attention 
upon  the  relevant  facts  and  so  to  discriminate  as  to  exclude 
from  consciousness,  for  the  time  being  at  least,  all  irrelevant 
details.  The  lack  of  such  a discriminating  faculty  leads 
either  to  error,  or  to  the  dearth  of  all  significant  results.  It 
is  necessary  to  avoid  either  extreme,  so  that  there  may  be  a 
sweeping  survey  of  all  the  possible  facts  relevant  to  the 
subject  under  investigation,  combined  at  the  same  time  with 
a concentration  of  attention  that  is  the  prerequisite  of  a 
deep  insight  into  the  inner  connections  and  interrelations  of 
these  facts.  There  must  be  a depth  as  well  as  a wideness 
of  vision. 

There  are  also  errors  arising  from  a failure  to  note 
significant  differences  in  phenomena  that  present  striking 
surface  resemblances.  Here  the  closest  scrutiny  is  necessary. 
The  older  chemists  could  not  distinguish  potash  from  soda ; 
baryta  and  strontia  were  formerly  confounded  together,  so 
also  potash  and  caesia.  Throughout  the  whole  realm  of 
scientific  research,  it  should  be  ever  kept  prominently  in 


362 


INDUCTIVE  LOGIC 


mind  that  surface  differences  may  hide  essential  resem- 
blances, and  that  surface  resemblances  may  hide  essential 
differences. 

3.  Errors  may  arise  from  apperceptive  projection.  Here 
the  objective  elements  of  perception  combine  with  the 
subjective,  so  that  the  complete  perception  may  contain 
elements  which  do  not  correspond  with  reality.  The  mind 
thus  projects  upon  the  field  of  vision  its  own  coloring.  We 
see  often  that  which  we  wish  to  see,  and  fail  to  see  that 
which  we  do  not  wish  to  see.  When  palladium  was  origi- 
nally made  known  to  the  public,  Cheuevix  proceeded  to 
examine  it,  prepossessed  with  the  idea  that  it  was  an  alloy 
of  some  two  known  metals.  This  idea  was  so  projected 
upon  his  experiments,  that  he  at  last  came  to  the  conclusion 
that  it  was  a compound  of  platinum  and  mercury.  Chene- 
vix  was  led  into  an  error  of  observation,  as  was  afterwards 
proved  by  Dr.  Wollaston,  who  himself  had  obtained  palla- 
dium from  the  solution  of  crude  platina  in  aqua  regia.1 
This  error  of  observation  was  due  to  the  fact  that  he 
approached  the  experiments  with  a fixed  idea  in  his  mind 
as  to  what  they  should  prove  ; and  being  determined  to  see 
evidences  of  this  in  the  phenomena,  he  unconsciously  read 
into  them  that  which  was  not  really  there. 

II.  Errors  of  Judgment.  — These  errors  occur  in  the 
interpretation  of  the  data  of  perception.  For  that  which  is 
observed  must  be  referred  to  its  appropriate  place  in  the 
body  of  knowledge  regarded  as  a system,  in  which,  part 
must  fit  to  part,  and  part  to  whole.  Inaccurate  reference 
results  in  manifest  imperfections  and  incongruities  in  that 
part  of  the  system  of  knowledge  to  which  the  reference  has 
been  made.  And  the  inferences  based  thereupon  are 
naturally  affected  by  this  fundamental  error  of  judgment. 
These  errors  are  as  follows : — 

1.  Errors  due  to  false  associations.  Here,  where  artifi- 
cial or  superficial  associations  are  interpreted  as  though  they 
1 Gore,  The  Art  of  Scientific  Discovery. 


INDUCTIVE  FALLACIES 


365 


were  real  causal  connections,  the  mistake  may  prove  most 
serious.  The  most  fertile  source  of  such  fallacies  is  the 
wrong  interpretation  of  space  and  time  associations,  regard- 
ing mere  contiguity  in  space  and  time  as  evidence  of  causal 
connection.  Under  this  head  may  be  classed  the  fallacies, 
non  causa  pro  causa  and  post  hoc  ergo  propter  hoc.  Pros- 
perity, for  instance,  following  the  enactment  of  certain  in- 
dustrial or  tariff  measures,  is  often  attributed  as  the  effect 
of  the  same,  merely  because  they  appear  in  striking  sequence. 
However,  it  may  be  that  the  prosperity  has  followed  in  spite 
of  the  laws  and  not  on  account  of  them. 

2.  Errors  of  judgment  due  to  emotional  perturbations. 
When  the  intellect  is  deflected  from  its  true  pointing  by 
passion,  or  prejudice,  or  superstition,  or  any  strong  emotion, 
the  consequent  judgment  is  the  resultant  of  two  forces, 
rather  than  the  expression  of  one.  As  Bacon  says : “ The 
human  understanding  resembles  not  a dry  light,  but  admits 
a tincture  of  the  will,  and  passions  which  generate  their 
own  systems  accordingly;  for  man  always  believes  more 
readily  that  which  he  prefers ; his  feelings  imbue  and  cor- 
rupt his  understanding  in  innumerable  and  sometimes  im- 
perceptible ways.” 1 

The  necessity  of  judging  in  a “ dry  light,”  as  far  as  pos- 
sible, is  especially  emphasized  in  the  ethical  positions  of 
Adam  Smith,  and  later  of  Mr.  Sidgwick.  Adam  Smith  con- 
tends that  one’s  duty  must  be  estimated  from  the  standpoint 
of  an  impartial  spectator  and  critic.  That  is,  man  must,  as 
it  were,  step  out  of  himself,  leaving  feeling  behind,  and 
judge  of  himself  and  of  his  duty  from  a purely  objective 
point  of  view.  So  also  Mr.  Sidgwdck  says  that  one  of  the 
chief  difficulties  in  the  utilitarian  position,  namely,  the  dis- 
crepancy between  the  egoistic  and  altruistic  claims  upon  our 
activities,  cannot  be  harmonized  satisfactorily,  when  stated 
as  a problem  of  mere  feeling.  Here  again  man  must  elimi- 
nate feeling  and  judge  of  himself  merely  as  one  among  many, 
1 Bacon,  Novum  Organum,  Book  I,  Aphorism  XLIX. 


364 


INDUCTIVE  LOGIC 


where  each  counts  for  one  and  no  one  for  more  than  one. 
In  the  light  of  pure  reason  he  may  be  able  to  see  that  the 
good  of  all  is  his  highest  good.  But  when  that  dry  light  is 
colored  by  feeling,  such  judgment  is  impossible. 

Faraday,  in  his  Observations  on  Mental  Education,  has 
borne  testimony  directly  to  the  necessity  of  eliminating  feel- 
ing from  our  judgments.  He  says:  “The  tendency  to  de- 
ceive ourselves  regarding  all  we  wish  for  should  be  kept  in 
mind,  and  the  necessity  also  of  resistance  to  these  desires. 
The  force  of  the  temptation  which  urges  us  to  seek  for  such 
evidence  and  appearances  as  are  in  favor  of  our  desires,  and 
to  disregard  those  which  oppose  them,  is  wonderfully  great. 
In  this  respect  we  are  all  more  or  less  active  promoters  of 
error.  I will  simply  express  my  strong  belief  that  that 
point  of  self-education  which  consists  in  teaching  the  mind 
to  resist  its  desires  and  inclinations  until  they  are  proved 
to  be  right,  is  the  most  important  of  all,  not  only  in  things 
of  natural  philosophy,  but  in  every  department  of  daily 
life.” 1 

3.  Errors  of  judgment  due  to  the  common  frailties  of 
human  nature.  Such  errors  Bacon  has  styled  “ Idols.”  His 
enumeration  is  not  only  complete,  but  is  classic  in  its  way, 
and  therefore  I quote  it  at  this  place : “ Four  species  of  idols 
beset  the  human  mind,  to  which,  for  distinction’s  sake,  we 
have  assigned  names,  calling  the  first  Idols  of  the  Tribe, 
the  second  Idols  of  the  Den,  the  third  Idols  of  the  Market, 
the  fourth  Idols  of  the  Theatre. 

“ The  formation  of  notions  and  axioms  on  the  foundation 
of  true  induction  is  the  only  fitting  remedy  by  which  we 
can  ward  off  and  expel  these  idols.  It  is,  however,  of  great 
service  to  point  them  out ; for  the  doctrine  of  idols  bears 
the  same  relation  to  the  interpretation  of  nature  as  that  of 
the  confutation  of  sophisms  does  to  common  logic.  The 
idols  of  the  tribe  are  inherent  in  human  nature,  and  the 
very  tribe  or  race  of  man ; for  man’s  sense  is  falsely  asserted 
1 Gladstone,  Michael  Faraday,  p.  128. 


INDUCTIVE  FALLACIES 


365 


to  be  the  standard  of  things ; on  the  contrary,  all  the  percep- 
tions, both  of  the  senses  and  the  mind,  bear  reference  to 
man  and  not  to  the  universe,  and  the  human  mind  is  like 
those  uneven  mirrors  which  impart  their  own  properties  to 
different  objects  from  which  rays  are  emitted,  and  distort 
and  disfigure  them. 

“ The  idols  of  the  den  are  those  of  each  individual,  for 
everybody  (in  addition  to  the  errors  common  to  the  race  of 
man)  has  his  own  individual  den  or  cavern  which  intercepts 
and  corrupts  the  light  of  nature,  either  from  his  own  peculiar 
and  singular  disposition,  or  from  his  education  and  inter- 
course with  others,  or  from  his  reading,  and  the  authority 
acquired  by  those  whom  he  reverences  and  admires,  or  from 
the  different  impressions  produced  on  the  mind  as  it  hap- 
pened to  be  preoccupied  and  predisposed,  or  equable  and 
tranquil,  and  the  like ; so  that  the  spirit  of  man  (according 
to  its  several  dispositions)  is  variable,  confused,  and  as  it 
were  actuated  by  chance ; and  Heraclitus  said  well  that  men 
search  for  knowledge  in  lesser  worlds,  and  not  in  the  greater 
or  common  world. 

“ There  are  also  idols  formed  by  the  reciprocal  intercourse 
and  society  of  man  with  man,  which  we  call  idols  of  the 
market,  from  the  commerce  and  association  of  men  with 
each  other;  for  men  converse  by  means  of  language,  but 
words  are  formed  at  the  will  of  the  generality,  and  there 
arises  from  a bad  and  unapt  formation  of  words  a wonder- 
ful obstruction  to  the  mind.  Nor  can  the  definitions  and 
explanations  with  which  learned  men  are  wont  to  guard  and 
protect  themselves  in  some  instances,  afford  a complete 
remedy,  — words  still  manifestly  force  the  understanding, 
throw  everything  into  confusion,  and  lead  mankind  into  vain 
and  innumerable  controversies  and  fallacies. 

“Lastly,  there  are  idols  which  have  crept  into  men’s 
minds  from  the  various  dogmas  of  peculiar  systems  of  phi- 
losophy, and  also  from  the  perverted  rules  of  demonstration, 
and  these  we  denominate  idols  of  the  theatre;  for  we  re- 


366 


INDUCTIVE  LOGIC 


gard  all  the  systems  of  philosophy  hitherto  received  or  im- 
agined, as  so  many  plays  brought  out  and  performed,  creating 
fictions  and  theatrical  worlds.  Nor  do  we  allude  merely  to 
general  systems,  but  also  to  many  elements  and  axioms  of 
sciences  which  have  become  inveterate  by  tradition,  implicit 
credence,  and  neglect.” 1 

All  such  tendencies,  as  thus  presented  by  Bacon,  clog  and 
hamper  the  normal  functioning  of  the  judgment.  The  mind 
must  be  alert  and  on  guard  to  eliminate  such  fatal  seeds  of 
error. 

III.  Errors  due  to  the  Imagination.  — Here  the  imagina- 
tion supplies  inner  connections  and  relations,  lying  beyond 
the  sphere  of  observation,  in  order  to  explain  the  nature  of 
the  observed  phenomena  themselves.  The  danger  here  is 
that  the  elements  supplied  in  order  to  make  the  self-con- 
sistent whole  do  not  correspond  to  reality.  The  system, 
regarded  as  a mental  construction,  may  be  complete  in  all 
of  its  coordinated  parts,  and  nevertheless  possess  no  objec- 
tive reality.  Under  this  head  fall  all  loosely  constructed 
hypotheses.  In  the  framing  of  an  hypothesis  in  general, 
the  imagination  functions  very  largely.  It  is  the  inner 
vision  that  represents  to  the  mind  the  things  not  seen. 
Moreover,  the  imagination  is  peculiarly  liable  to  error,  and 
to  swing  clear  of  the  trammels  of  fact,  and  in  the  region  of 
pure  fancy  construct  systems  that  rest  upon  no  solid  basis 
of  reality.  These  dangers  in  detail  have  been  pointed  out 
in  the  chapter  on  hypothesis. 

The  most  fertile  source  of  error,  however,  arises  from 
that  natural  elation  of  mind  upon  the  discovery  even  of 
slight  confirming  evidence  of  the  truth  of  the  assumed 
hypothesis.  This  enthusiasm  is  apt  to  magnify  unduly  an 
inadequate  verification,  and  to  rest  satisfied  in  an  hypothesis 
that  is  grounded  upon  an  insufficient  basis.  Thus,  since  the 
year  1770,  more  than  forty  discoveries  of  new  elementary 
substances  have  been  announced  to  the  world  by  enthusi- 
1 Bacon,  Novum  Organum,  Book  I,  Aphorisms  XXXIX,  etc. 


INDUCTIVE  FALLACIES 


367 


astic  experimenters,  and,  in  all  cases,  tlieir  discoveries  have 
been  proved  to  be  absolutely  worthless.  For  instance,  it  was 
confidently  announced  that  Torbern  Bergmann,  in  1777,  bad 
extracted  from  diamonds  what  he  considered  to  be  a new 
earth,  and  called  it  “terra  nobilis.”  Wedgwood,  in  1790, 
discovered  “ australia  ” in  sand  obtained  from  the  continent 
of  that  name;  but  Hatchett  proved  it  to  be  merely  a mix- 
ture of  silica,  alumina,  oxide  of  iron,  and  plumbago.  In 
1805  Richter  discovered  “ niccolanium  ” ; it  was  afterwards 
proved  to  be  a mixture  of  iron,  cobalt,  nickel,  and  arsenic. 
These  instances  are  but  a few  of  the  many  which  charac- 
terize the  history  of  chemical  research,  and  stand  as  con- 
spicuous witnesses  of  the  danger  of  divorcing  fancy  from 
fact. 

The  imagination  however  properly  constrained  is  most 
potent  in  suggesting  possible  causal  relations,  in  construct- 
ing hypotheses,  in  devising  methods  of  experiment  in  order 
to  verify  them,  and  in  forming  universal  concepts  in  which 
all  the  particulars  of  observation  must  coinhere.  Davy  and 
Faraday  were  both  conspicuous  in  this  mental  characteristic. 
And  to  this  source  their  eminent  discoveries  may  be  traced. 
Dr.  Whewell  says,  for  instance,  of  Faraday : “ In  discover- 
ing the  nature  of  voltaic  action,  the  essential  intellectual 
requisite  was  to  have  a distinct  conception  of  that  which 
Faraday  expressed  by  the  remarkable  phrase,  ‘ An  axis  of 
power  having  equal  and  opposite  forces.’  And  the  distinct- 
ness of  this  idea  in  Faraday’s  mind  shines  forth  in  every 
part  of  his  writings.  He  appears  to  possess  the  idea  of  this 
kind  of  force  with  the  same  eminent  distinctness  with  which 
Archimedes  in  the  ancient  and  Stevinus  in  the  modern  his- 
tory of  science  possessed  the  idea  of  pressure,  and  were  thus 
able  to  found  the  idea  of  mechanics.  And  when  Faraday 
cannot  obtain  these  distinct  modes  of  conception,  he  is  dis- 
satisfied and  conscious  of  defect.”  1 

It  is  indeed  a touch  of  genius  that  enables  one  to  grasp 
1 Whewell,  History  of  Inductive  Sciences,  Vol.  Ill,  3d  ed.,  p.  147. 


368 


INDUCTIVE  LOGIC 


and  formulate  a central  idea  that  will  unify  and  also  uni- 
versalize  a large  body  of  seemingly  disconnected  and  incon- 
gruous facts.  But  such  an  idea  must  be  the  expression  of 
the  relations  actually  obtaining,  and  no  subjective  fancy 
projected  upon  the  phenomena  themselves,  however  clever 
or  ingenious  such  an  imaginative  creation  may  be.  If  one 
were  asked  what  is  the  most  efficient  instrument  of  scientific 
research,  the  answer  must  be,  “ The  Imagination ! ” And  if 
one  were  asked  what  is  the  most  fertile  source  of  error,  the 
answer  likewise  must  be,  “ The  Imagination ! ” It  must 
also  be  remembered  that  it  is  not  sufficient  merely  that  an 
hypothesis  should  be  in  harmony  with  the  facts  in  the  case ; 
it  must  be  proved,  also,  that  the  facts  are  connected  with 
the  hypothesis  through  necessary  links. 

And  it  is  well,  also,  to  bear  this  in  mind  when  arguing 
against  a rival  hypothesis  that  may  have  been  advanced  by 
an  opponent  who  has  claimed  for  it  only  the  possibility  of 
its  validity,  and  who  has  not  affirmed  its  necessity.  It  is 
manifestly  unfair,  as  well  as  fallacious,  to  deny  the  possi- 
bility of  the  hypothesis  merely  by  indicating  certain  un- 
certainties connected  with  establishing  it.  To  contradict 
possibility,  one  must  prove  the  hypothesis  impossible.  Re- 
garding such  a conflict  between  rival  hypotheses  Ueberweg 
suggestively  comments  as  follows:  “In  cases  of  this  kind, 
it  is  one  of  the  hardest  of  scientific  and  ethical  problems  to 
give  fair  play  to  one’s  opponent.  Our  own  prejudices  are 
sure  to  influence  us.  Yet  the  effect  of  the  influence  of  an- 
other’s standpoint,  when  it  is  reached,  is  of  immense  value  in 
scientific  knowledge.  Polemic  easily  leads  to  exaspera- 
tion ; it  is  easy  both  to  abuse  it  and  to  let  it  alone  because 
of  dislike  to  the  conflicts  which  it  produces ; but  it  is 
difficult  to  recognize  it,  and  use  it  in  the  right  sense  as 
the  necessary  form  which  the  labor  of  investigation  always 
takes.  Man  never  attains  to  a scientific  knowledge  of  the 
truth  without  a rightly  conducted  battle  of  scientifically 
justifiable  hypotheses,  the  one  against  the  other : the 


INDUCTIVE  FALLACIES 


369 


scientific  guidance  of  this  battle  is  the  true  dialectic 
method.” 1 

IV.  Errors  of  the  Conceptual  Processes.  — This  class  of 
errors  arises  in  the  formation  of  general  concepts  and  their 
expression  in  universal  laws.  The  natural  tendency  of  the 
mind  to  generalize  often  leads  to  ill-considered  results.  The 
universal  unites  many  differences  into  an  identity,  and  the 
mind  will  readily  minimize  the  differences  in  order  to  form 
a desired  universal ; thus  disparate  attributes  may  be  incor- 
rectly coordinated  in  one  and  the  same  system.  Herschel 
has  remarked  that  hasty  generalization  is  the  bane  of  science. 
And  Bacon  has  said  our  intellects  want  not  wings,  but  rather 
weights  of  lead  to  moderate  their  course. 

The  method  of  agreement,  when  relied  upon  to  the  exclu- 
sion of  further  experimental  determination,  is  a fertile  source 
of  error  in  this  respect.  The  possibility  of  a plurality  of 
causes  should  be  ever  kept  prominently  in  mind.  One 
readily  assigns  an  effect  to  a causal  element  which  is  only 
partially  its  cause ; the  consequent  generalization  is,  there- 
fore, incorrect.  For  instance,  it  often  happens  that  activities 
of  young  animals  are  described  as  instinctive  and  congenital ; 
and  universal  propositions  are  founded  thereupon.  And  yet 
it  may  be  that  the  activities  referred  solely  to  instinct  are 
due  partially  to  imitation.  In  order  to  avoid  this  error  and 
eliminate  the  factor  of  imitation,  investigators  in  this  line 
are  accustomed  to  study  the  activities  of  animals  hatched  in 
incubators  and  purposely  kept  from  all  of  their  kind.  This 
illustration  will  serve  to  show  the  precautions  that  must  be 
taken  in  order  to  eliminate  all  possible  error  from  the  data 
which  the  process  of  generalization  constructs  into  universal 
forms.  So  also  inaccuracies  in  any  of  the  other  inductive 
methods  lead  to  gross  errors  in  the  consequent  generaliza- 
tions based  upon  them. 

Under  this  head,  also,  are  the  fallacies  resulting  from  the 
extension  of  empirical  laws  to  spheres  beyond  the  experience 
1 Ueberweg,  A System  of  Logie,  etc.,  p.  509. 


370 


INDUCTIVE  LOGIC 


which  they  embody  and  express.  This  source  of  error  is 
especially  illustrated  in  laws  expressing  some  quantitative 
relation  between  antecedent  and  consequent;  it  is  a natural 
supposition  in  such  cases,  and  yet  a misleading  one  often- 
times, that  a simple  proportional  relation  will  exist  between 
phenomena  of  the  same  nature,  but  with  greater  or  lesser 
magnitude,  as  the  case  may  be.  Bacon  gives  the  following 
illustrations  of  this  fallacy : “ Suppose  a leaden  ball  of  a 
pound  weight,  let  fall  from  a steeple,  reaches  the  earth  in 
ten  seconds,  will  a ball  of  two  pounds,  where  the  power  of 
natural  motion,  as  they  call  it,  should  be  double,  reach  it  in 
five  ? No,  they  will  fall  almost  in  equal  times,  and  not 
be  accelerated  according  to  quantity.  Suppose  a drachm  of 
sulphur  would  liquefy  half  a pound  of  steel,  will,  therefore, 
an  ounce  of  sulphur  liquefy  four  pounds  of  steel?  It  does 
not  follow;  for  the  stubbornness  of  the  matter  in  the  patient 
is  more  increased  by  quantity  than  the  activity  of  the  agent. 
Besides,  too  much  as  well  as  too  little  may  frustrate  the 
effect,  — thus,  in  smelting  and  refining  of  metals  it  is  a 
common  error  to  increase  the  heat  of  the  furnace  or  the 
quantity  of  the  flux ; but  if  these  exceed  a due  proportion, 
they  prejudice  the  operation,  because  by  their  force  and  cor- 
rosiveness they  turn  much  of  the  pure  metal  into  fumes, 
and  carry  it  off,  whence  there  ensues  not  only  a loss  in  the 
metal,  but  the  remaining  mass  becomes  more  sluggish  and 
intractable.  Men  should,  therefore,  remember  how  iEsop’s 
housewife  was  deceived,  who  expected  that  by  doubling  her 
feed  her  hen  should  lay  two  eggs  a day ; but  the  hen  grew 
fat  and  laid  none.  It  is  absolutely  unsafe  to  rely  upon  any 
natural  experiment  before  proof  be  made  of  it,  both  in  a less 
and  a larger  quantity.” 1 

Another  fallacy  of  the  same  order  often  occurs  in  the 
inference  concerning  the  interpolated  elements  of  a series 
whose  successive  values  have  not  all  been  observed.  The 
inference  extends  the  nature  of  the  known  to  the  unknown 
1 Bacon,  Advancement  of  Learning,  Book  V,  Chap.  II,  p.  190. 


INDUCTIVE  FALLACIES 


371 


parts,  and  presumes  that  the  intermediate  links  between 
actually  observed  parts  of  the  series  are  in  accordance  with 
the  general  nature  of  the  latter.  Such  inferences  very  often 
give  correct  results,  as,  in  the  plotting  of  a curve,  some 
salient  points  may  be  determined  according  to  observed 
quantitative  variations,  and  the  remaining  portions  sup- 
plied, as  upon  the  above  supposition.  This  extension  to 
cover  intermediate  and  unobserved  instances  may,  however, 
be  sometimes  very  fallacious.  For  a force  may  be  assumed 
to  be  such  that  its  effects  increase  steadily,  and  it  may  be 
that  they  operate  periodically  ; interpolation  upon  one  as- 
sumed basis  when  the  other  is  the  true  one  would  of  course 
introduce  grave  errors.  To  eliminate  such  errors,  devices 
have  in  many  cases  been  resorted  to  by  which  a self-regis- 
tering apparatus  will  record  all  successive  values  of  the 
phenomena  under  investigation. 

Under  the  fallacies  of  hasty  generalization  naturally  fall 
all  provincialisms  which  arise  from  a narrow  nature  and 
habit  of  mind.  The  local  traditions  and  superstitions,  the 
prevailing  winds,  the  social  customs  and  manners,  are  taken 
as  types  of  a universal  experience.  The  inferential  widen- 
ing of  the  circle  of  a limited  experience  is  always  provocative 
of  false  inference  and  misleading  results. 

We  have  also  false  analogies  which  consist  in  the  ex- 
tension of  our  experience  of  certain  phenomena  that  we 
have  observed  to  be  alike  in  some  respects  to  include  other 
attributes  not  observed,  concerning  which  we  assume  a 
corresponding  similarity ; the  abuse  of  final  causes  may  be 
regarded  as  a special  case  of  false  analogy.  Moreover,  a 
tendency  to  consider  causation  in  the  light  exclusively  of 
final  causes  has  often  retarded  the  advance  of  science, 
in  withdrawing  the  attention  and  energies  of  the  investi- 
gator from  a search  after  physical  causes,  as,  for  in- 
stance, among  the  ancients  it  was  declared  that  the  leaves 
of  the  trees  are  to  defend  the  fruit  from  the  sun  and 
wind.  Besting  satisfied  in  such  an  explanation,  the  pre- 


372 


INDUCTIVE  LOGIC 


cise  function  of  the  leaves  in  the  economy  of  the  plant’s 
growth  was  not  further  investigated,  and  thus  progress  was 
impossible. 

Again,  incorrect  classification  is  a source  of  error.  In 
grouping  together  disparate  phenomena,  we  have  a basis  for 
forming  a generic  concept  that  will  include  incompatible 
species,  or,  in  other  words,  a universal  that  will  have  evi- 
dent exceptions.  Moreover,  if  the  classification  is  partial, 
the  resulting  laws  based  upon  it  will  have  only  empirical 
force. 

I have  endeavored  in  this  chapter  to  indicate  errors  that 
are  mainly  psychological  in  their  origin,  for  two  reasons. 
In  the  first  place,  such  errors  operate  as  disturbing  forces 
in  the  midst  of  purely  logical  processes.  The  data  of  in- 
ference are  psychological  as  regards  their  source,  and  errors 
thus  originating  affect  the  inference  based  upon  them, 
appearing  in  the  final  result  as  logical  fallacies.  An  error 
of  observation  becomes  an  error  in  the  judgment  that  is 
based  upon  the  original  perception,  and  perdures  in  the 
hypothesis,  classification,  etc.,  founded  on  that  judgment, 
and  finally  emerges  in  the  conclusions  based  upon  these 
processes.  In  the  second  place,  the  fallacies  that  are  purely 
formal,  and  in  the  strict  sense  logical,  are  not  as  apt  to 
deceive  and  mislead  the  mind.  In  the  material  data  espe- 
cially lurk  the  germs  of  fallacy.  On  the  theory  that  it  is 
wiser  and  also  more  logical  to  stamp  out  an  error  in  its 
incipiency,  I have  placed  special  emphasis  upon  the  various 
psychological  processes  as  initial  sources  of  error.  More- 
over, it  is  more  rational  to  deal  with  errors  of  process  rather 
than  flaws  of  product.  A machine  that  turns  out  imperfect 
articles  could  have  its  imperfections  rectified  by  repairing 
each  article  thus  produced ; or  the  machine  itself  could  be 
readjusted  so  as  to  produce  the  articles  without  flaw.  It  is 
needless  to  say  which  method  is  the  more  logical,  and  most 
satisfactory,  as  well. 

The  desideratum  is  accurate  and  comprehensive  observa- 


INDUCTIVE  FALLACIES 


373 


tion;  a discriminating  judgment  formed  in  the  “ dry  light” 
of  reason ; an  imagination  that  has  deep  insight  into  the 
heart  of  surface  appearances ; and  powers  of  generalization 
which  transcend  observed  phenomena  by  adequately  inter- 
preting them. 


CHAPTER  XVII 


THE  INDUCTIVE  METHODS  AS  APPLIED  TO  THE  VARI- 
OUS SCIENCES 

The  nature  of  each  separate  science  will  determine  cer- 
tain peculiarities  of  method  for  that  science ; and  its  pecul- 
iar method  will  be  largely  a matter  of  growth,  as  experience 
accredits  or  discredits  the  various  results  which  its  opera- 
tion may  attain.  It  will  thus  be  corrected  or  supplemented 
according  as  it  stands  the  test  of  achieved  results.  There 
are,  however,  some  general  features,  and  especially  some 
natural  limitations  of  the  inductive  methods,  that  may  be 
properly  indicated. 

I.  In  the  first  place,  the  nature  of  the  method  used,  and 
its  efficiency,  as  measured  by  its  results,  will  be  found  to 
vary  as  the  nature  of  the  phenomena  themselves.  Some 
phenomena  admit  of  analysis  and  determination  by  experi- 
ment. Instead  of  attempting  to  determine  the  relation  of 
a complex  antecedent  to  a complex  consequent,  the  antece- 
dent is  first  separated  into  its  component  parts,  and  each 
element  is  tested  alone  in  order  to  disclose  its  precise  effect. 
The  relation  can  then  be  expressed  between  the  simple 
antecedent  and  simple  consequent,  as  a causal  connection ; 
and  it  admits,  moreover,  of  a quantitative  determination  as 
well.  Such  a method  of  procedure  by  analytical  experiment 
enables  us  to  rise  to  laws  having  universal  validity.  This 
method  is  characteristic,  especially,  of  the  physical  sciences, 
because  the  phenomena  readily  admit  of  resolution  into 
component  parts,  and  the  isolation  of  one  simple  force  so 
as  to  determine  its  total  effect.  The  physical  forces  are 
most  readily  adaptable  to  experiment.  They  therefore 

374 


INDUCTIVE  METHODS  AND  THE  SCIENCES  375 


afford  the  widest  field  for  the  application  of  the  experi- 
mental method  of  inductive  inquiry.  Moreover,  we  may 
readily  predict  the  results  of  a combination  of  simple  forces, 
when  we  know  the  laws  governing  their  component  elements. 
The  inducto-deductive  method,  therefore,  becomes  especially 
efficient  in  extending  the  domain  of  the  physical  sciences. 
Here,  also,  mathematical  analysis  and  calculation  is  most 
valuable  as  an  aid  to  experimental  investigation,  and  in 
determining  quantitative  relations  as  necessitated  by  the 
mathematical  laws  to  which  the  data  gathered  inductively 
must  conform. 

There  are  however  sciences  which  present  phenomena 
of  such  a high  degree  of  complexity  that  an  analysis  of  a 
complex  whole  into  its  separate  parts  or  elements  of  force 
is  impossible.  Moreover,  the  phenomena  cannot  be  ana- 
lyzed so  that  a certain  part  of  the  complex  whole  can  be 
indicated  as  the  complete  antecedent,  and  the  remaining 
portion  as  the  entire  consequent.  The  difficulty  therefore 
is  twofold;  it  is  impossible  to  separate  the  complex  whole 
into  two  other  complex  wholes,  antecedent  and  consequent, 
and  still  further  impossible  to  separate  such  antecedent  and 
consequent,  even  if  they  could  be  determined,  into  their 
simplest  component  parts.  The  phenomena  presented  are 
here  not  in  the  form  of  a sequence  so  often  as  in  that  of 
coexistence,  as  in  the  sciences  of  botany,  zoology,  and  the 
like.  Here  the  methods  of  analogy  and  classification  must 
be  resorted  to,  and  we  obtain  descriptive  laws  as  the  result. 

The  forces  manifested  in  the  processes  of  vital  growth 
are  especially  difficult  to  determine  by  experiment ; for  they 
not  only  operate  to  produce  certain  effects,  but  are  conserved 
in  the  effects  so  as  to  produce  certain  other  effects  in  a pro- 
cess of  continuous  construction.  Separation  by  mechanical 
analysis  means  instant  cessation  of  the  process  itself.  Dis- 
section means  death.  Here  then  is  a natural  limitation. 
Moreover,  the  laws  of  development  are  further  modified  by 
external  changes.  The  result  of  the  inner  force  and  the 


376 


INDUCTIVE  LOGIC 


outer  influences  working  together  complicates  the  prob- 
lems to  such  an  extent  that  the  pure  inductive  methods  are 
well-nigh  impossible  of  application.  Resort  is  then  had  to 
determination  by  statistical  methods.  Large  groups  of 
plants  and  animals  are  examined  for  the  purpose  of  noting 
tendencies  disclosed  in  the  aggregate,  but  hidden  as  regards 
their  manifestation  in  the  individual.  Here  of  course  classi- 
fication is  an  aid  in  disclosing  similarities  and  differences 
that  may  suggest  hypotheses  to  explain  certain  dominant 
characteristics. 

We  may  moreover  have  merely  permanent  effects  pre- 
sented in  perception,  the  cause  having  ceased  to  act  long 
since.  Thus  in  geology  we  have  facts  that  have  been  caused, 
it  is  true,  but  the  causes  can  be  discerned  only  as  manifested 
in  the  effects,  and,  therefore,  they  can  be  determined  only  by 
the  method  of  hypothesis,  which  may  lead  to  verification  or 
not,  as  the  case  may  be.  Again,  certain  sciences  may  suggest 
problems  which  concern  the  explanation  or  significance,  not 
of  particular  phenomena  within  the  sphere  of  that  science, 
but  rather  the  interpretation  of  the  whdle  body  of  phenom- 
ena which  the  science  in  question  comprehends.  The  prob- 
lem is  not  solved,  therefore,  by  any  attempt  in  the  way  of 
analysis  by  experiment,  but  rather  in  the  way  of  synthesis 
through  hypothesis,  that  is,  the  ideal  construction  of  a whole 
which  will  unify  and  account  for  all  facts,  or,  in  other  words, 
the  disclosing  of  the  system  which  underlies  and  coordi- 
nates the  various  particular  manifestations.  This  is  espe- 
cially illustrated  in  the  problems  which  geology  and  biology 
present  concerning  the  interpretation  of  their  respective 
phenomena  regarded  in  the  light  of  their  totality.  Astron- 
omy also  presents  a mass  of  seemingly  chaotic  phenomena, 
and  yet  the  aim  of  this  science  is  to  reduce  them  all  to  some 
one  self-consistent  system. 

For  instance,  Mr.  Spencer  remarks  concerning  the  general 
nature  of  biological  study : “ In  like  manner  biology  is  the 
elaboration  of  a complete  theory  of  life  in  each  and  all  of 


INDUCTIVE  METHODS  AND  THE  SCIENCES  377 


its  involved  manifestations.  If  different  aspects  of  its  phe- 
nomena are  investigated  apart,  if  one  observer  busies  himself 
in  classing  organisms,  another  in  dissecting  them,  another  in 
ascertaining  their  chemical  compositions,  another  in  study- 
ing functions,  another  in  tracing  laws  of  modification,  — 
they  are  all  consciously  or  unconsciously  helping  to  work 
out  a solution  of  vital  phenomena  in  their  entirety,  both 
as  displayed  by  individual  organisms  and  by  organisms  at 
large.” 1 

Mr.  Spencer,  as  we  have  seen  in  the  chapter  on  division, 
makes  the  distinction  between  investigation  of  particular 
causal  relations  on  the  one  hand,  and,  on  the  other,  the  in- 
terpretation of  the  total  phenomena  of  a science,  as  the  basis 
for  his  classification  of  the  sciences. 

The  division  of  Herbert  Spencer  can  only  be  accepted  in  a 
general  way  as  indicating  predominant  characteristics  of  the 
two  kinds  of  sciences.  It  will  not  do  to  lay  down  hard  and 
fast  lines  here,  for  every  science  presents  two  kinds  of  prob- 
lems ; the  first,  to  determine  particular  causal  relations  ; the 
second,  to  coordinate  all  such  relations  into  a self-consistent 
system  which  will  unify  all  separate  and  individual  instances. 
For  instance,  take  the  phenomena  of  light  in  physics  ; par- 
ticular problems  as  regards  intensity,  velocity,  composition 
of  light,  etc.,  present  themselves  ; then  an  underlying  prob- 
lem, How  explain  all  the  phenomena  of  light  upon  some  one 
single  basis  regarding  the  essential  nature  of  light  ? Hence 
arose  the  emission  and  undulatory  theories  of  light,  and  all 
phenomena  bearing  upon  the  theory  were  marshalled  in  sup- 
port of  one  and  of  the  other,  until  the  conflict  was  conclu- 
sively decided.  And  again,  the  theory  of  light,  the  theory 
of  electricity,  the  theory  of  heat,  etc.,  suggest  still  another 
problem,  How  unify  all  the  separate  theories  in  one  all- 
comprehensive  theory  to  which  the  separate  phenomena 
may  be  alike  referred  ? thus  every  science  presents  particu- 
lar problems,  and  a general  problem  as  well.  And  herein 
1 Spencer,  Classification  of  the  Sciences,  pp.  19,  20. 


378 


INDUCTIVE  LOGIC 


lies  a suggestion  that  all  investigators  in  any  branch  of 
science  would  do  well  to  bear  in  mind.  Specialization  in 
any  one  line  of  particular  problems  should  always  lead  to  a 
consideration  of  the  relations  of  these  particular  problems 
to  the  general  system  of  which  they  are  parts.  Specializa- 
tion that  does  not  thus  supply  its  own  corrective  by  the 
natural  insistence  of  the  mind  to  interpret  the  particular 
in  the  light  of  more  general  laws,  tends  to  narrowness  of 
mind  and  barren  results. 

II.  In  reference  to  method  in  the  sciences  it  must  be 
observed  also  that  in  certain  phenomena  the  simple  theory, 
which  regards  the  causal  connection  as  a transfer  of  energy 
according  to  the  doctrine  of  the  conservation  of  energy,  is 
further  complicated  by  certain  variations  and  modifications 
of  the  energy  in  the  process  of  transference.  When,  for 
instance,  a billiard-ball  strikes  another,  and  the  second  ball, 
by  virtue  of  the  impact,  receives  the  energy  of  the  initial 
moving  ball  transferred  to  it,  the  problem  is  simplified  by 
the  fact  that  the  motion  of  the  first  is  easily  traceable  in 
the  second,  being  a transfer  of  energy  which  manifests  it- 
self in  the  same  manner  in  the  two  cases.  However,  the 
problem  is  complicated  at  once  when  in  chemistry,  for  in- 
stance, the  two  combining  elements  form  a third  in  which 
the  characteristic  features  of  the  former  are  wholly  lost  in 
the  new  form.  Here  is  likewise  a transfer  of  energy,  which 
may  have  mechanical  equivalents,  it  is  true,  and  yet  so 
radical  a change  of  form  accompanies  the  transfer  that  it 
complicates  the  problems  which  arise  in  this  science.  We 
have  seen  how  the  combined  inducto-deductive  method  often 
predicts  events  and  the  nature  of  phenomena  not  yet  ob- 
served. And  yet  this  becomes  most  difficult  whenever 
transfer  of  energy  is  accompanied  by  a change  in  the 
peculiarities  of  its  manifestation  as  well.  Knowledge  of 
the  nature  of  two  elements,  and  all  their  separate  charac- 
teristics, will  not  be  sufficient  data  for  any  prediction  as  to 
the  nature  of  the  compound.  Thus  chemistry  confronts  a 


INDUCTIVE  METHODS  AND  THE  SCIENCES  379 


natural  difficulty  as  regards  method,  which  does  not  affect 
physical  science  generally. 

Another  difficulty  appears  in  psychology,  for  here  stimuli 
from  the  outer  world,  expressed  in  terms  of  physical  energy 
and  quantitatively  determined,  produce  psychical  reactions, 
that  cannot  be  expressed  in  physical  terms.  And,  on  the 
other  hand,  processes  of  ideation  produce  muscular  activi- 
ties, that  may  be  estimated  in  physical  terms.  It  has  been 
urged  that  here  the  theory  of  conservation  of  energy  breaks 
down,  that  the  transferred  energy  is  wholly  accounted  for  by 
the  nerve  and  brain  modifications,  and  that  the  psychical  ac- 
companiments are  wholly  unaccounted  for  upon  this  basis. 
They  stand  out  as  unexplored  remainders. 

This  objection  is  met  in  two  ways.  One  is  that  the 
physical  and  psychical  are,  as  it  were,  two  closed  circles, 
and  while  simultaneous  in  their  functioning  do  not  mutually 
interact.  This  is  the  theory  of  the  so-called  “ psychophysi- 
cal parallelism.”  It  necessitates  metaphysical  explanations 
and  postulates  that  seem  to  complicate  rather  than  simplify 
the  difficulties.  The  second  is  the  more  reasonable,  that 
psychical  activity  may  be  radically  different  from  physical 
and  yet  the  two  capable  of  reacting  upon  each  other,  so  as 
to  liberate  the  potential  activities  in  either  sphere,  and  thus 
initiate  a series  of  causally  connected  phenomena.  Such  a 
theory  is  buttressed  by  substantial  analogies  in  the  physical 
sphere  itself;  namely,  that  in  many  phenomena  the  imping- 
ing force  is  so  modified,  by  the  reaction  due  to  the  nature  of 
the  substance  acted  upon,  as  to  lose,  to  all  observation  at 
least,  its  original  characteristic  features.  For  instance, 
friction  passes  over  into  electricity  because  of  the  nature  of 
the  substance  that  is  rubbed ; thunder  sours  cream,  and  thus 
sound  vibrations  cause  effects  wholly  incongruous  to  them. 

These  illustrations  might  be  multiplied  through  all  the 
realm  of  physical  science.  They  are  so  many  as  to  prepare 
us  for  realizing  the  possibility,  at  least,  that  physical  excita- 
tions may  produce  psychical  phenomena  in  the  sense  that 


380 


INDUCTIVE  LOGIC 


the  outer  stimulus  calls  into  activity  psychical  energies,  that 
thus  stirred,  manifest  themselves  according  to  the  forms  of 
their  own  nature,  rather  than  the  forms  of  the  physical 
phenomena  exciting  them.  Upon  such  a theory  we  may 
proceed,  by  observation  and  experiment,  to  measure  dura- 
tion, intensity,  etc.,  of  mental  reactions  responding  to 
external  stimuli.  As  regards  the  method  here  employed, 
the  series  is  considered  as  one  and  complete,  so  that  physi- 
cal excitations  are  traced,  as  it  were,  through  an  unbroken 
causal  chain  to  their  psychical  effects,  and  vice  versa.  On 
the  theory  of  two  closed  circles,  it  is  difficult  to  indicate  a 
logical  method  of  experimental  inquiry,  unless  it  be  further 
postulated  that  activities  in  the  one,  according  to  its  kind, 
may  induce  modifications  of  the  other  according  to  its  kind. 
This  reservation  is  generally  insisted  upon. 

III.  It  sometimes  happens  that  the  phenomena  of  one 
science  are  to  be  interpreted  in  the  light  of  the  results  of 
another  science.  Thus  the  laws  of  one  science  become  guid- 
ing principles  in  investigating  the  causal  relations  existing 
in  another  sphere.  This  can  only  be  done  when  there  is 
some  similarity  between  the  phenomena  of  the  two  sciences. 
This  method  is  especially  illustrated  in  historical  explana- 
tion. The  problem  presents  a mass  of  events  that  must  be 
coordinated  in  a system  wherein  their  several  causal  rela- 
tions will  be  exhibited.  And  not  merely  must  detached 
epochs  be  proved  interrelated  as  regards  the  events  occurring 
in  them,  but  here,  also,  the  special  problems  give  rise  to  a 
general  problem,  to  discover  in  the  whole  the  underlying 
philosophy  of  history,  and  to  determine  the  several  histori- 
cal tendencies  in  one  system  whose  characteristic  features 
will  reveal  the  fact  that  “ through  the  ages  one  increasing 
purpose  runs.” 

To  solve  the  special  and  the  general  problems  of  history, 
recourse  is  had  to  an  analysis  of  events  on  the  basis  of  well- 
established  psychological  results.  The  phenomena  of  his- 
tory are  substantially  the  activities  of  man,  both  in  his 


INDUCTIVE  METHODS  AND  THE  SCIENCES  381 


individual  and  collective  capacities.  Events  being  given, 
an  hypothesis  concerning  the  motives,  and  ends  which 
actuated  them,  is  framed  upon  the  supposition  that  men 
ordinarily  are  impelled  by  similar  motives  under  similar 
circumstances,  in  order  to  achieve  similar  ends.  Here  the 
analogies  drawn  between  men  of  the  present  and  men  of  the 
past,  or  between  men  moving  in  the  ordinary  routine  of 
everyday  life  and  men  whose  acts  may  be  epoch-making, 
furnish  a basis  for  historical  interpretation.  We  say  that  a 
series  of  events,  perhaps  of  a very  complicated  nature,  can 
be  explained  only  by  an  hypothesis  that  a well-defined  pur- 
pose and  a strong  determined  will  were  fashioning  them  and 
moving  through  them  to  an  end  that  was  in  the  chief  actor’s 
mind  from  the  beginning.  And  so  the  rise  of  social  habits, 
customs,  traditions,  laws,  the  religion,  the  government,  and 
national  institutions  of  a people  have  an  origin  in  psychical 
and  not  physical  elements,  a deeper  understanding  of  whose 
nature  and  all  that  it  necessitates  tends  to  a clearer  elucida- 
tion of  the  problems  therein  presented.  The  knowledge  of 
man,  the  microcosm,  is  a guiding  thread  amid  the  bewilder- 
ing mazes  of  the  macrocosm.  It  is  possible,  of  course,  for 
the  imagination  of  the  historian  to  lead  him  to  wander  far 
afield,  and  invent  fanciful  motives,  purposes,  public  poli- 
cies, etc.,  to  explain  given  events.  However,  here,  as  in 
the  physical  and  other  sciences,  the  hypotheses  framed  must 
meet  the  general  requirements  and  conditions  of  a valid 
hypothesis. 

IV.  There  has  been  a growing  tendency  in  sciences  re- 
garded as  solely  or  largely  deductive,  to  correct  and  supple- 
ment the  traditional  method  and  results  by  a more  searching 
inductive  inquiry.  This  is  especially  true  of  political 
economy.  The  deductive  method  proceeded  to  build  up  a 
body  of  doctrine  composed  of  inferences  necessitated  by  a 
few  fundamental  premises.  The  premises  were  such  as  the 
following : The  principal  motive  of  action  is  self-interest ; 
the  earth,  as  man’s  great  supply-house,  is  limited  in  extent 


382 


INDUCTIVE  LOGIC 


and  productivity ; the  physical  and  psychological  tendencies 
of  man  lead  him  to  multiply  his  own  species  with  a rapidity 
which,  if  not  counteracted  by  obstacles,  would  bring  about 
an  unlimited  increase  of  population.  All  economic  laws 
were  thus  deduced  from  some  such  fundamental  propositions 
as  these.  The  results  of  this  deductive  method,  however, 
have  been  brought  to  the  bar  of  another  method  for  search- 
ing examination  and  judicial  sentence.  In  1848  Hildebrand, 
and  Knies  in  1853,  with  Roscher  in  1854,  set  forth  the  prin- 
ciples of  the  historical  school  of  political  economy.  They 
held  that  an  inductive  inquiry  must  be  started  in  order  to 
estimate  the  physical,  ethnical,  and  historical  conditions  of 
a nation  and  its  stage  of  civilization.  These  forces,  correctly 
assessed,  will  give  the  economic  conditions  of  a particular 
period  of  history,  or  of  a particular  nation.  This  is  not  the 
place  to  criticise  the  tenets  of  this  school,  but  merely  to 
point  out  the  fact  that  its  influence  has  been  potent  in  cor- 
recting and  supplementing  the  results  obtained  in  a purely 
deductive  manner. 

Deduction  may  give  the  joint  effect  of  universal  psycho- 
logical impulses,  operative  under  certain  natural  conditions 
of  environment,  etc.,  provided  no  disturbing  force  is  present. 
But  the  question  here  is  not  whether  a certain  cause,  if  act- 
ing alone,  will  produce  a certain  effect ; but  whether  coun- 
teracting causes  will  be  present,  or  modifying  causes,  as  the 
case  may  be.  To  estimate  the  results  of  collocations  and 
not  simple  causes  becomes,  as  we  have  seen,  a complex 
problem.  For  its  solution  recourse  must  be  had  largely  to 
statistical  methods  whereby  large  aggregates  reveal  ten- 
dencies that  are  actual  and  not  theoretical  merely. 

In  a similar  way,  the  historical  school  of  jurisprudence, 
associated  with  Savigny,  has  influenced  the  so-called  philo- 
sophical school  in  demonstrating  that  results  theoretically 
determined  by  deduction  are  constantly  modified  by  the  real 
conditions  and  limitations  of  each  particular  nation’s  life. 
The  influence  of  this  school  is  indicated  by  a significant 


INDUCTIVE  METHODS  AND  THE  SCIENCES  383 


fact,  that  when  Hegel  wrote  his  theory  of  law  ( Rechtslehre ) 
he  paid  more  regard  to  the  historical  formation  of  states 
than  did  the  earlier  theorists  of  natural  law.1 

Again,  another  illustration  of  the  growing  prevalency  of  in- 
ductive method  is  found  in  the  modern  psychological  method. 
The  sole  method  was  considered  from  time  immemorial  to  be 
that  of  introspection.  Its  results,  however,  were  meagre  ; 
the  method  itself  was  indefinite  and  lacked  certainty  and 
uniformity.  Inductive  inquiry  therefore  proceeded  by  its 
own  methods  to  secure  and  interpret  material  in  other  and 
various  fields.  As  Professor  Ladd  says:  “The  method  of 
psychological  science  is  peculiarly  introspective  and  analytic 
of  the  envisaged  phenomena  called  states  of  consciousness. 
But  it  is  far  broader  and  more  effective  than  it  could  be  if 
it  were  merely  introspective.  It  pushes  its  analysis  of  the 
genesis  of  the  phenomena  as  far  back  as  possible,  by  the  use  of 
experimental  methods,  and  methods  of  external  observation 
applied  to  the  whole  process  of  mental  evolution  (study  of 
infants,  of  primitive  man,  and  of  the  lower  animals,  — evo- 
lutionary and  comparative  psychology).  It  interprets  the 
psychological  life  of  the  individual  mind  in  the  light  of  knowl- 
edge gathered  concerning  the  psychical  development  of  the 
race  (the  psychological  study  of  literature,  society,  art,  reli- 
gion, etc.).  It  lays  peculiar  emphasis  upon  abnormal  and 
pathological  phenomena  of  the  nervous  and  mental  life 
(psychiatry,  hypnotism,  phenomena  of  insanity  and  of  the 
criminal  classes,  etc.).  It  takes  account  of  the  rise  and  fall 
of  particular  forms  of  psychological  theory  (the  history  of 
psychology).  It  strives  to  transcend  experience  by  hypo- 
thetical principles  of  explanation.  But  in  the  employment 
of  all  these  methods  this  science  differs  in  no  important 
respect  from  the  sciences  which  deal  wholly  with  physical 
phenomena.  It  is  only  the  use  of  introspection  for  the 
possession,  and,  to  some  extent  at  least,  for  the  analysis,  of 


1 Bluntschli,  The  Theory  of  the  State,  p.  69. 


884 


INDUCTIVE  LOGIC 


its  objects,  which  makes  psychology,  as  respects  its  method, 
different  from  the  other  sciences.”  1 

In  the  above,  we  see  that  inductive  inquiry  lays  all  pos- 
sible fields  of  research  under  tribute  to  the  one  end  of  ex- 
plaining and  correlating  psychical  phenomena.  The  systems 
of  ethics  also,  which  are  founded  upon  an  a priori  basis,  are 
becoming  more  indebted  to  empirical  investigations  which 
have  given  a richer  content  to  the  strictly  formal  ethic. 
Advanced  psychological  research,  the  study  of  race  char- 
acteristics, tribal  customs,  habits,  law,  religion,  etc.,  the 
indications  of  moral  progress, — all  give  material  which,  if 
interpreted  by  right  hypotheses,  will  throw  light  upon  the 
theory  of  ethical  principles  regarded  merely  from  a specula- 
tive point  of  view.  We  may  conclude,  therefore,  that  the 
inductive  method  and  the  deductive  are  not  mutually  exclu- 
sive processes.  They  may  be  so  combined  as  mutually  to 
strengthen  one  another.  What  Bluntschli  says  of  jurispru- 
dence may  be  applied  equally  as  well  to  all  sciences  that 
claim  some  a priori  basis : “ The  old  strife  between  the 
philosophical  and  historical  schools  in  Germany  has  alto- 
gether ceased.  Peace  was  made  as  early  as  1840.  Since 
then  it  is  recognized  on  all  sides  that  the  experiences  and 
phenomena  of  history  must  be  illumined  with  the  light  of 
ideas,  and  that  speculation  is  childish  if  it  does  not  con- 
sider the  real  conditions  of  the  nation’s  life.”  2 

It  will  be  seen  how  important  a factor  historical  data  be- 
come in  all  the  sciences  that  deal  with  human  volition  and 
activities.  Whatever  hypothesis  may  be  framed,  it  must 
correspond  to  these  data,  because  they  represent  actual  con- 
ditions that  must  be  coordinated  in  a self-consistent  system, 
and  their  nature  and  relations  must  admit  of  satisfactory 
interpretation. 

1 Ladd,  Introduction  to  Philosophy , p.  116. 

2 Bluntschli,  The  Theory  of  the  State,  p.  70. 


CHAPTER  XVIII 


HISTORICAL  SKETCH  OF  INDUCTION 

Socrates  (470-399  b.c.).  — We  find  the  beginnings  of 
inductive  inquiry  in  the  Socratic  or  maieutic  method,  that 
art  of  mental  midwifery  by  which  conceptions  were  to  be 
delivered  from  the  mass  of  individual  experiences  and 
opinions  in  which  they  lie  concealed.  The  Socratic  pro- 
cedure in  the  formation  of  conceptions  is  to  question  every 
particular  view,  and  estimate  it  by  bringing  together  analo- 
gous cases,  and  discovering  their  natural  connections,  so  as 
to  explicate  the  general  notion  which  it  contains,  and  thus 
proceed  from  comparison  of  particulars  to  the  framing  of 
general  propositions.  Socrates’s  generalizations  were  many 
of  them  hasty,  and  in  his  desire  to  formulate  a general  con- 
ception he  overlooked  exceptions  and  minimized  difficulties, 
but  in  his  method  there  were  the  germs  of  truly  scientific 
procedure.  The  sphere  of  his  method  was,  however,  lim- 
ited, as  he  applied  it  only  to  the  illumination  of  ethical 
controversies. 

Plato  (427-347  b.c.).  — Plato  enriched  the  Socratic  method 
of  induction  by  removing  its  limitation  to  ethical  inquiry. 
Plato  was  especially  concerned  with  investigating  the  rela- 
tions of  his  “ ideas  ” to  each  other,  and  this  led  to  the 
apprehension  of  the  logical  relations  between  conceptions, 
especially  as  regards  their  subordination  and  coordination. 
This  forms  a basis  for  classification,  — Plato’s  division  of 
class-concepts  or  logical  genera  into  their  species  is  a promi- 
nent feature  of  his  method.  He  also  suggests  the  hypotheti- 
cal method  of  treating  the  relations  of  concepts ; namely,  to 
examine  a tentatively  proposed  conception  by  developing 

385 


386 


INDUCTIVE  LOGIC 


all  the  possible  consequences  that  would  follow  from  its 
union  with  known  conceptions.  This  is  in  keeping  with 
the  inducto-deductive  method  of  Mill  and  the  modern 
logicians. 

Aristotle  (384-322  b.c.).  — Aristotle’s  name  is  especially, 
and  it  may  be  said  almost  exclusively,  associated  with 
deductive  logic  and  syllogistic  reasoning.  Although  he  did 
not  develop  fully  the  inductive  logic,  he  nevertheless  did 
not  ignore  it,  in  some  of  its  essential  features  at  least.  He 
acknowledged  the  necessity  of  investigating  the  starting- 
point  of  deduction,  namely,  the  ultimate  grounds  of  proof, 
and  of  the  principles  of  explanation.  This  process  he  called 
dialectic.  It  is  a double  process  that  proceeds  from  the 
particulars  given  in  perception,  and  from  the  ideas  current 
in  customary  opinion,  to  discover  the  general,  and  then 
from  the  general  to  deduce  the  particular,  which  is  thereby 
verified  in  the  process.  The  former  procedure  is  the  reverse 
of  the  deductive,  and  is  epagogic  or  inductive.  Induction, 
according  to  him,  is  a syllogism  in  which  the  inference  that 
the  major  belongs  to  the  middle,  is  mediated  through  the 
minor  directly;  and  not  indirectly  through  the  middle. 
Thus,  to  use  Aristotle’s  illustration,  the  investigation  of  the 
connection  between  the  absence  of  gall  in  animals  and  lon- 
gevity in  a number  of  instances,  as  in  man,  horse,  mule,  etc., 
may  disclose  their  coexistence.1  They  are  then  united 
directly  without  mediation  of  a middle  term.  If  we  had 
given  the  universal  proposition  to  start  with,  Whatever 
animal  has  no  gall  is  long-lived,  and  the  minor  premise  that 
man,  horse,  mule,  etc.,  are  animals  having  no  gall,  then  the 
conclusion  would  follow,  therefore  they  are  long-lived.  This 
is  the  deductive  syllogism.  The  inductive  method,  on  the 
other  hand,  starts  from  particular  observation  that  the  horse 
which  has  no  gall  is  long-lived,  so  also  the  mule,  so  also 
man,  etc. ; therefore,  without  any  middle  term,  a coexistence 
is  taken  as  equivalent  to  a causal  relation  between  these 
1 Aristotle,  Prior  Analytics , II.  xxiii. 


HISTORICAL  SKETCH  OF  INDUCTION 


387 


attributes,  and  the  inference  is  drawn  that  all  animals 
having  no  gall  are  long-lived.  Such  an  inference  is  valid 
syllogistically,  however,  only  on  the  assumption  that  the 
instances  examined  comprise  the  whole  class  having  the 
attributes  under  investigation.  This  inductive  syllogism, 
therefore,  expresses  inferences  only  of  complete  enumeration. 

The  form  of  such  a syllogism  is  as  follows : — 

Let  S = minor  term, 

P = major  term, 

M = middle  term. 

This,  that,  and  the  other  S is  P. 

This,  that,  and  the  other  S is  all  M. 

All  M is  P. 

Here  it  will  be  observed  that  the  particular  instances 
comprising  the  minor  term  S,  when  summed  up,  equal  the 
middle  term.  There  is  no  inference  in  this  if  we  have 
regard  to  the  strict  sense  in  which  the  word  is  used. 
Aristotle,  indeed,  considered  the  only  scientific  induction 
to  be  the  so-called  perfect  induction,  and  says  that  to 
generalize  many  experiences  of  the  same  kind  is  admissible 
only  when  there  is  no  contrary  case.  The  thought  that  the 
proof  of  causal  connection  enables  us  to  generalize  is  stated 
by  Aristotle,  but,  as  Ueber weg  says,  it  “does  not  attain  to 
a fundamental  significance  in  his  logical  theory.”1 

The  Precursors  of  Bacon.  — The  revolt  against  the  scho- 
lasticism of  the  Middle  Ages  and  the  fetters  of  the  Aristote- 
lian logic  was  many-voiced,  culminating,  however,  as  regards 
the  emphasis  placed  upon  induction  as  a scientific  method, 
in  the  works  of  Francis  Bacon. 

Foremost  among  the  early  champions  of  inductive  inquiry 
we  find  Boger  Bacon,  born  in  1214,  a Franciscan  monk,  yet 
devoted  heart  and  mind  to  the  cause  of  science.  His  Opus 
Majus  was  published  first  in  1733  by  Dr.  S.  Jebb,  princi- 
pally from  a manuscript  in  the  library  of  Trinity  College, 
1 Ueberweg,  Logic,  p.  479. 


388 


INDUCTIVE  LOGIC 


Dublin.  This  work  is  characterized  by  a spirit  of  protest 
against  authority  in  general,  and  that  of  Aristotle  and  his 
logic  especially.  He  recommends  mathematics  and  experi- 
ment as  the  two  great  instruments  of  scientific  investigation. 
In  this  particular  it  is  interesting  to  note  his  anticipation 
of  the  modern  mathematico-physical  modes  of  scientific  in- 
quiry. The  following  quotation  will  give  an  indication  of 
his  spirit  and  aims  : — 

“ Experimental  science,  the  sole  mistress  of  speculative 
sciences,  has  three  great  prerogatives  among  other  parts  of 
knowledge : First,  she  tests  by  experiment  the  noblest  con- 
clusions of  all  other  sciences ; next,  she  discovers,  respect- 
ing the  notions  which  other  sciences  deal  with,  magnificent 
truths  to  which  these  sciences  of  themselves  can  by  no 
means  attain ; her  third  dignity  is,  that  she  by  her  own 
power,  and  without  respect  of  other  sciences,  investigates 
the  secrets  of  nature.” 1 

Leonardo  da  Vinci  (1452-1519).  — Leonardo  combined 
in  one  personality  many  brilliant  talents,  being  eminent  as 
sculptor,  painter,  architect,  engineer,  astronomer,  and  natural 
philosopher.  His  works,  unpublished,  exist  in  manuscripts 
in  the  library  of  the  Institute  at  Paris.  He  expresses  him- 
self very  clearly  and  emphatically  concerning  the  relation 
of  experience  to  speculation : “ Theory  is  the  general ; ex- 
periments are  the  soldiers.  We  must  consult  experience, 
and  vary  the  circumstances  till  we  have  drawn  from  them 
general  rules ; for  it  is  she  who  furnishes  true  rules.  But 
of  what  use,  you  ask,  are  these  rules  ? I reply,  that  they 
direct  us  in  the  researches  of  nature  and  the  operations  of 
art.  They  prevent  our  imposing  upon  ourselves  and  others, 
by  promising  ourselves  results  which  we  cannot  obtain. 
But  see  the  absurdity  of  men ! They  turn  up  their  noses 
at  a man  who  prefers  to  learn  from  nature  herself  rather 
than  from  authors  who  are  only  her  clerks.”  2 This  latter 

1 Whewell,  Philosophy  of  the  Inductive  Sciences,  Vol.  II,  p.  369. 

2 Ibid.,  Vol.  II,  p.  369. 


HISTORICAL  SKETCH  OF  INDUCTION 


389 


remark  is  similar  in  its  reference  to  the  epithet  of  Galileo, 
applied  to  men  whose  knowledge  comes  wholly  from  books 
and  not  from  observation ; namely,  “ paper  philosophers.” 
Bernardinus  Telesms  (1508-1588).  — His  work,  entitled 
De  Rerum  Natura,  anticipated,  in  some  degree  at  least,  the 
Novum  Organum  of  Bacon.  Bacon  himself  says  of  him : 
“We  think  well  concerning  Telesins,  and  acknowledge  him 
as  a lover  of  truth,  a useful  contributor  to  science,  an 
amender  of  some  tenets,  the  first  of  recent  men.”  Telesius 
set  for  himself  a high  aim  and  purpose,  but  in  the  applica- 
tion of  his  method  he  was  not  so  fortunate,  being  dominated 
in  his  researches  by  speculation  rather  than  the  results  of 
experimental  inquiry.  As  to  his  professed  method,  he  an- 
nounces in  the  title  of  his  Be  Natura  that  “ the  construction 
of  the  world,  the  magnitude  and  nature  of  the  bodies  con- 
tained in  it,  are  not  to  be  investigated  by  reasoning,  which 
was  done  by  the  ancients,  but  are  to  be  apprehended  by  the 
senses  and  collected  from  the  things  themselves.”  And  in  the 
Proem  of  the  same  work  he  says  in  a like  strain  that  “ they 
who  before  us  have  inquired  concerning  the  construction  of 
this  world,  and  of  the  things  which  it  contains,  seem  indeed 
to  have  prosecuted  their  examination  with  protracted  vigils 
and  great  labor,  but  never  to  have  looked  at  it.  For,  as  it 
were,  attempting  to  rival  God  in  wisdom,  and  venturing  to 
seek  for  the  principles  and  causes  of  the  world  by  the  light 
of  their  own  reason,  and  thinking  they  had  found  what  they 
had  only  invented,  they  made  an  arbitrary  world  of  their 
own.  We  then,  not  relying  on  ourselves,  and  of  a duller 
intellect  than  they,  propose  to  ourselves  to  turn  our  regards 
to  the  world  itself  and  its  parts.” 

Following  Telesius,  and  of  his  school,  was  Thomas  Cam- 
panella  ( 1568-1639).  He  was  a contemporary  of  Bacon, 
and,  under  the  influence  of  Telesius,  early  conceived  the 
idea  of  an  inductive  method  of  research.  At  the  age  of 
twenty-two,  he  published  a work  whose  character  may  be 
judged  by  its  title,  — “ Thomas  Campanella’s  Philosophy 


390 


INDUCTIVE  LOGIC 


demonstrated  to  the  senses,  against  those  who  have  philos- 
ophized in  an  arbitrary  and  dogmatical  manner,  not  taking 
nature  for  their  guide ; in  which  the  errors  of  Aristotle  and 
his  followers  are  refuted  from  their  own  assertions  and  the 
laws  of  nature ; and  all  the  imaginations  feigned  in  the 
place  of  nature  by  the  Peripatetics  are  altogether  rejected; 
with  a true  defence  of  Bernardin  Telesius  of  Cosenza,  the 
greatest  of  philosophers;  confirmed  by  the  opinions  of  the 
ancients,  here  elucidated  and  defended,  especially  those  of 
the  Platonists.” 

The  ideas  of  Bacon,  with  their  impetus  to  the  inductive 
method  of  research,  were  not  only  anticipated  by  writers  of 
books  ; but  actual  discoveries  by  zealous  investigators  were 
turning  the  attention  of  the  thinking  world  to  nature  and 
her  secrets.  There  was  an  illustrious  line  of  pioneers  in 
this  undiscovered  country.  There  was  Andrew  Csesalpinus 
(1520-1603),  the  founder  of  the  science  of  botany;  and 
earlier,  Copernicus  (1473-1543),  advancing  his  heliocentric 
theory ; and  Gilbert  (1540-1603),  the  court  physician  of 
Elizabeth  and  James,  conducting  with  untiring  perseverance 
his  investigations  of  the  nature  of  magnetism  and  electricity. 
Kepler,  born  ten  years  after  Bacon,  1571,  and  Galileo,  born 
in  1564,  and  their  contemporary,  Tycho  Brahe,  born  in 
1546,  formed  a triumvirate  of  scientific  power  and  brill- 
iancy, made  resplendent  by  the  glory  of  the  heavens 
itself.  It  must  be  remembered,  too,  that  at  this  time  a new 
world  had  been  discovered  across  the  seas;  the  recent  in- 
ventions of  gunpowder,  of  the  mariner’s  compass,  and  of 
the  art  of  printing,  all  tended  to  stimulate  the  thought 
of  the  world,  and  usher  in  a new  epoch  in  the  history 
of  civilization. 

Francis  Bacon  (1561-1626). — Bacon’s  inductive  system 
is  given,  for  the  most  part,  in  the  Novum  Organum.  The 
title  of  this  work  was  in  itself  a protest  against  Aristotle 
and  his  logic,  implying  that  Aristotle’s  Organon  was  now 
out  of  date  and  was  to  be  superseded  by  the  new.  Bacon 


HISTORICAL  SKETCH  OF  INDUCTION 


391 


insists  that  all  knowledge  of  nature  has  for  its  end  the  dis- 
closing of  the  causes  of  things.  According  to  the  Aristote- 
lian scheme,  causes  are  formal,  material,  efficient,  or  final. 
Bacon  is  only  concerned  with  the  formal  causes.  For,  he 
says,  all  events  have  their  ground  in  the  “ forms  ” of 
things.  By  the  form  of  a thing,  he  meant  its  essential 
nature.  Where  he  uses  the  form  we  may  well  supply  the 
word  law.  To  discover  the  forms  of  phenomena,  it  is  nec- 
essary, according  to  Bacon,  to  collect  as  many  instances  as 
possible  in  which  the  phenomenon  under  investigation  ap- 
pears ; together  they  form  a tabula  prcesentice.  In  like  man- 
ner, the  instances  in  which  the  phenomenon  is  lacking  are 
grouped  in  a tabula  absentice;  and  a third  group  must  be 
formed,  — a tabula  graduum  in  which  the  variations  of 
intensity  in  the  phenomena  are  compared  with  the  varying 
intensity  of  other  phenomena.  The  problem  is  then  to  be 
solved  by  a process  of  exclusion  ( exclusio ) ; that  is,  the 
rejection  or  exclusion  of  the  several  qualities  which  are  not 
found  in  some  instance  where  the  given  quality  is  present, 
or  are  found  in  some  instance  where  the  given  quality  is 
absent,  or  are  found  to  increase  in  some  instance  where  the 
given  quality  decreases,  or  to  decrease  when  the  given  qual- 
ity increases.  By  this  process  an  indication  will  be  given 
by  which  an  hypothesis  may  be  framed,  and  finally  verified 
by  subsequent  observation  and  experiment.  In  the  sketch 
of  this  method  it  will  be  seen  that  his  three  tables  of  in- 
stances closely  resemble  the  methods  of  agreement,  of  dif- 
ference, and  of  concomitant  variations.  They,  however, 
lack  the  precision  of  the  later  formulation  of  these  methods. 
There  is  no  hint  at  a systematic  selection  and  variation  of 
the  instances ; and  no  requirement,  as  in  the  method  of  dif- 
ference, that  two  instances  shall  be  so  experimentally  de- 
termined that  they  will  agree  in  every  point  save  the  given 
phenomenon,  which  is  present  in  the  one  and  absent  from 
the  other.  Bacon,  however,  made  a substantial  contribu- 
tion to  the  method  of  induction  in  general,  in  insisting  upon 


392 


INDUCTIVE  LOGIC 


the  examination  of  instances  themselves,  and  in  ascending 
from  them  quite  gradually  the  scale  of  the  more  general 
up  to  the  most  general,  and  in  this  he  entered  a vigorous 
protest  against  hasty  generalization. 

As  to  the  manner  of  certifying  the  hypothesis  formed 
after  the  process  of  collecting  and  sifting  instances,  Bacon 
has  no  recourse  to  deduction  based  upon  the  hypothesis  and 
consequent  verification.  He  seems  to  despise  mathematical 
method  as  an  ally  of  inductive  inquiry ; and  therefore  has 
no  place  in  his  scheme  for  the  prediction  of  new  phenomena 
by  means  of  calculation.  Of  his  nine  divisions  of  aids  to 
induction,  he  completed  only  the  first,  — Prerogative  In- 
stances. Of  the  instances  which  he  enumerates,  twenty- 
seven  in  all,  only  a few  have  any  bearing  directly  upon  the 
inductive  method  proper.  Two  sets  of  these  instances  may 
be  considered  as  a crude  statement  of  the  methods  of  agree- 
ment and  difference ; the  Solitary  Instances,  which  either 
exhibit  a phenomenon  without  any  of  its  usual  accompani- 
ments or  which  agree  in  everything  except  some  particular 
phenomenon,  and  Migratory  Instances,  where  qualities  are 
produced  in  bodies  by  evident  causes,  as,  for  instance,  the 
producing  of  whiteness  by  pounding  glass,  also  by  stirring 
water  into  froth.  These  instances  however  as  exhibited 
by  Bacon  lack  precision  and  the  possibilities  of  accurate 
determination  of  causal  connections.  The  only  other  group 
of  instances  having  special  inductive  significance  is  that  of 
the  Instantia  Crucis;  as  before  mentioned,  such  instances  are 
valuable  in  deciding  between  rival  hypotheses.  With  all  the 
deficiencies  of  Bacon’s  method,  however,  his  service  to  the 
thinking  world  is  indisputable,  in  emphasizing  the  need  of 
investigating  phenomena  themselves  as  a corrective  of  fanci- 
ful speculations,  and  in  his  vigorous  warnings  against  preju- 
dice, against  intellectual  indolence,  against  subjection  of  the 
mind  to  the  trammels  of  authority,  and  against  over  hasty 
generalizations. 

Locke  (1632-1704).  — Locke  applied  the  method  of  Bacon 


HISTORICAL  SKETCH  OF  INDUCTION 


393 


to  the  objects  of  inner  experience.  He  declared  that  the 
data  of  all  knowledge  come  from  sensation,  or  sense-percep- 
tion, and  from  reflection,  and  that  there  are  no  “innate 
ideas,”  and  therefore  no  starting-point  for  a priori  specula- 
tions. The  method  that  had  been  found  useful  in  actual 
discoveries,  such  as  those  of  Newton,  Kepler,  and  others, 
Locke  insisted  would  prove  productive  also  of  rich  results 
in  the  intellectual  sphere. 

Isaac  Newton  (1642-1727).  — Scientific  method  was  grad- 
ually formulating  itself  in  the  actual  pursuits  of  scientific 
investigation,  — not  thought  out  as  much  as  worked  out,  and 
its  efficiency  tested  and  confirmed  by  results.  Newton  gives 
form  to  that  which  was  a result  of  many  experiments,  and 
of  a mass  of  various  experiences,  in  his  Rules  of  Philoso- 
phizing (Regulce  Philosophandi ) prefixed  to  the  Principia. 

These  rules  are  as  follows  : — 

1.  The  first  rule  is  twofold : — 

a.  “ Only  real  causes  are  to  be  admitted  in  explanation  of 
phenomena.” 

b.  “No  more  causes  are  to  be  admitted  than  such  as 
suffice  to  explain  the  phenomena.” 

2.  “In  as  far  as  possible,  the  same  causes  are  to  be 
assigned  for  the  same  kind  of  natural  effects.” 

3.  “ Qualities  that  can  neither  be  increased  nor  dimin- 
ished in  intensity,  and  that  obtain  in  all  bodies  accessible  to 
experiment,  must  be  considered  qualities  of  all  bodies  what- 
soever.” 

4.  “In  philosophical  experiment,  propositions  collected 
from  phenomena  by  induction  are  to  be  held,  notwithstand- 
ing contrary  hypotheses,  as  either  exactly  or  approximately 
true,  until  other  phenomena  occur  whereby  they  are  either 
rendered  more  exact  or  are  proved  liable  to  exceptions.” 

New'ton’s  celebrated  saying,  “ Hypotheses  non  fingo,”  was 
originally  a protest  against  the  supposition  of  the  existence 
of  occult  or  imaginary  causes  to  explain  phenomena,  notably 


394 


INDUCTIVE  LOGIC 


the  Cartesian  explanation  of  the  celestial  movements  by 
vortices.  Hypotheses  of  a different  nature,  and  rationally 
grounded,  did  not  fall  under  Newton’s  reprehension. 

Sir  John  Herschel  (1792-1871).  — Herschel’s  Discourse 
on  the  Study  of  Natural  Philosophy  was  published  in  1832. 
John  Stuart  Mill  reviewed  this  book  in  the  Examiner,  and 
was  evidently  impressed  and  influenced  by  it.  Herschel’s 
design  was  to  make  the  methods  of  science  more  explicit. 
These  are  contained  in  nine  “ propositions  readily  applicable 
to  particular  cases,  or  rules  of  philosophizing.” 

Of  these  propositions,  the  second,  seventh,  eighth,  and 
ninth  present  substantially  the  experimental  methods  as 
afterwards  more  precisely  formulated  by  Mill.  These 
methods,  however,  he  regards  simply  as  means  to  discovery, 
and  not  methods  of  proof.  Of  the  remaining  propositions, 
the  first  is  a more  precise  statement  of  Bacon’s  principle 
of  exclusion,  and  is  the  foundation  of  the  joint  method  of 
agreement  and  difference.  The  third  proposition  is  that 
“ we  are  not  to  deny  the  existence  of  a cause  in  favor  of 
which  we  have  a unanimous  agreement  of  strong  analogies, 
though  it  may  not  be  apparent  how  such  a cause  can  pro- 
duce the  effect,  or  even  though  it  may  be  difficult  to  con- 
ceive its  existence  under  the  circumstances  of  the  case.” 
The  fourth  is  that  “contrary  or  opposing  facts  are  equally 
instructive  for  the  discovery  of  causes  with  favorable  ones.” 
The  fifth  recommends  the  “ tabulation  of  facts  in  the  order 
of  intensity  in  which  some  peculiar  quality  subsists.” 
The  sixth  rule  insists  upon  the  investigator  keeping  promi- 
nently in  mind  the  possibility  that  “counteracting  or  modi- 
fying causes  may  subsist  unperceived,”  and  that  this  fact 
may  be  the  means  of  explaining  many  apparent  excep- 
tions. 

Herschel  also  emphasizes  the  necessity  of  combining  in- 
duction and  deduction  in  complicated  inquiries ; and,  further, 
he  explains  the  nature  of  empirical  laws,  as  also  the  nature 
and  tests  of  hypotheses.  We  can  now  see  that  the  body  of 


HISTORICAL  SKETCH  OF  INDUCTION 


395 


inductive  principles  begins  at  length  to  assume  final  form 
and  proportion. 

Whewell  (1795-1866).  — Dr.  Whewell  published  his  Phi- 
losophy of  the  Inductive  Sciences  in  1840,  containing  his  sys- 
tem of  induction.  His  method  involves  two  principal 
processes,  — the  colligation  of  facts  and  the  explication  of 
conceptions.  The  investigator  is  to  gather  all  the  facts  at 
his  disposal,  and  upon  them  he  is  to  superinduce  a concep- 
tion which  will  unify  them,  or  colligate  them.  He  says 
these  conceptions  are  supplied  by  the  mind,  while  facts  are 
supplied  by  the  sense.  This  however  is  a distinction  that 
separates  so  widely  the  spheres  of  the  particular  facts,  and 
the  general  conceptions,  that  upon  such  a basis  a union  of 
the  two  as  explaining  one  by  the  other  would  be  artificial 
and  with  no  corresponding  bond  of  reality.  The  colligating 
conception  does  not  exist  in  the  mind  before  or  apart  from 
its  existence  in  fact.  The  attempt  to  fit  facts  to  ready-made 
conceptions  is  of  the  nature  of  guesswork.  Kepler’s  nine- 
teen guesses  regarding  planetary  orbits  is  an  instance  of 
attempting  to  superinduce  conceptions  upon  a mass  of  facts. 
It  is  not  a truly  scientific  or  logical  procedure,  and  the 
great  danger  of  applying  it  lies  in  the  fact  that  the  mind 
all  too  readily  tends  to  mould  facts  into  the  forms  of  prior 
conceptions. 

“The  Methods  employed  in  the  Formation  of  Science,” 
the  title  of  his  concluding  chapter,  are  three,  as  follows: 
Methods  of  Observation,  Methods  of  Obtaining  Clear  Ideas, 
and  Methods  of  Induction.  The  last  principally  concerns 
our  present  purposes.  The  methods  of  induction  are 
methods  of  discovery  rather  than  proof ; save  the  last,  which 
is  one  of  the  experimental  methods.  They  are,  the  method 
of  curves  to  express  graphically  the  graduated  results  of  sev- 
eral observations ; the  method  of  means,  and  the  method  of 
least  squares,  both  designed  to  eliminate  accidental  accom- 
paniments of  constant  causes  by  striking  an  average  of  sev- 
eral observations ; and  the  method  of  residues.  Whewell’s 


396 


INDUCTIVE  LOGIC 


method  may  be  characterized  in  brief  as  a method  of  discov- 
ery rather  than  proof. 

John  Stuart  Mill  (1806-1873).  — Mill’s  Logic,  published 
in  1813,  was  essentially  a method  of  proof  rather  than  a 
method  of  discovery.  His  aim  in  formulating  the  methods 
in  vogue  in  experimental  science,  was  to  discover  the  pre- 
cise modes  of  their  operation  in  order  to  apply  the  same  in 
investigating  the  various  mental,  moral,  social,  and  political 
phenomena.  Bacon  in  the  Novum  Organum  had  asserted 
that  this  inductive  method  was  applicable  to  the  intellectual 
and  moral  sciences.  This  was  no  doubt  suggestive  to  Mill, 
as  it  had  been  to  Locke.  Whately’s  Logic,  published  in 
1827,  influenced  Mill,  and  was  the  means  of  turning  his 
attention  to  logical  studies.  Whately’s  book  was  reviewed 
by  Mill,  when  only  twenty -one,  in  the  Westminster  Review. 
The  revival  in  logical  interest  at  this  time  and  the  depar- 
ture from  scholastic  traditions  have  been  traced  to  the  influ- 
ence of  Edward  Copleston,  tutor  at  Oxford,  and  afterwards 
Bishop  of  Llandaff.  Whately’s  work  represented  the  first- 
fruits,  and  Mill’s  the  richer  and  riper  product  of  this  revival 
of  logic.  It  is  a matter  of  more  than  passing  interest  to 
note  that  one  of  Whately’s  most  active  collaborators  in  the 
work  was  John  Henry  Newman,  so  that,  as  Professor  Minto 
says,  “ the  common  room  of  Oriel,  which  Mr.  Froude  de- 
scribes as  the  centre  from  which  emanated  the  High  Church 
Movement,  may  also  be  said  to  have  been  the  centre  from 
which  emanated  the  movement  that  culminated  in  the  revo- 
lution of  logic.” 

Mill’s  special  office  as  regards  induction  consists  in  his 
crystallizing  the  principles  and  practices  of  the  scientific 
investigators  who  had  caught  and  reflected  the  spirit  of 
modern  research.  The  formulated  methods  of  inductive 
logic,  substantially  as  given  by  Mill,  have  become  the 
recognized  methods  of  all  investigation  that  is  actuated  by 
a scholarly  spirit  and  a scientific  habit.  Mill’s  contribu- 
tions to  the  inductive  logic  have  been  so  largely  drawn 


HISTORICAL  SKETCH  OF  INDUCTION 


397 


from  and  so  frequently  referred  to  in  the  composition  of 
this  book,  as  to  need  no  further  comment  here.  The  works 
of  the  more  recent  writers,  as  Lotze,  Sigwart,  Bosanquet, 
Jevons,  Venn,  etc.,  have  also  been  noticed  in  the  body  of 
the  text.  Their  work  is  largely  critical,  and  no  distinct 
inductive  system  is  especially  associated  with  any  of  their 
names. 


LOGICAL  EXERCISES 


LOGICAL  EXERCISES 


PART  I 


1.  (a)  All  A is  B. 
All  B is  C. 
.•.  All  C is  A. 


(Z>)  All  A is  B. 


No  A is  C. 
•\  No  C is  B. 


(c)  All  A is  B. 


(d)  Some  A is  B. 


All  C is  B. 
All  C is  A. 


No  A is  C. 

Some  C is  not  B. 


2.  The  atmosphere  cannot  be  a conductor  of  electricity ; for 
metals  are  conductors  of  electricity,  and  the  atmosphere  is  of  course 
not  a metal. 

3.  If  there  is  to  be  any  appreciation  of  German  literature,  one 
must  be  conversant  with  the  German  language. 

A certain  man  has  a knowledge  of  the  German  language. 

.-.  He  appreciates  German  literature. 

4.  Whatever  is  opposed  to  our  industrial  prosperity  is  to  be  re- 
garded as  a serious  evil. 

All  European  wars  are  serious  evils. 

.-.  They  are  opposed  to  our  industrial  prosperity. 

5.  All  patrons  of  the  arts  and  sciences  are  public  benefactors. 

No  poor  men  are  patrons  of  the  arts  and  sciences. 

/.  No  poor  men  are  public  benefactors. 

6.  All  democrats  are  hostile  to  the  bill. 

All  beet-sugar  men  are  hostile  to  the  bill. 

.•.  All  beet-sugar  men  are  democrats. 

7.  Given  A is  B,  to  prove  B is  A. 

Now  B is  either  A or  not  A. 

If  B is  not  A,  then  by  -what  is  given  we  have  the  syllogism, 


A is  B. 

B is  not  A. 

A is  not  A,  which  is  absurd. 


Is  this  reasoning  correct  or  not  ? 


401 


— Professor  Jastrow, 


402 


LOGICAL  EXERCISES 


8.  The  courageous  are  confident  and  the  experienced  are  confi- 
dent. Therefore  the  experienced  are  courageous. 

9.  If  the  door  were  locked,  the  horse  would  not  be  stolen  ; but  the 
horse  is  not  stolen  ; therefore  the  door  must  have  been  locked. 

10.  Given  the  major  premise,  If  an  engineer  sees  a danger  signal, 
he  will  stop  the  train.  What  can  be  inferred  from  the  several  minor 
premises  as  follows : — 

(a)  He  saw  a danger  signal. 

(b)  He  did  not  see  a danger  signal. 

(c)  He  stopped  the  train. 

(d)  He  did  not  stop  the  train. 

11.  All  dishonest  men  are  immoral,  and  as  a certain  man  is  con- 
fessedly immoral,  it  follows  that  he  must  be  dishonest. 

12.  All  members  of  the  finance  committee  are  members  of  the 
executive  committee.  No  members  of  the  library  committee  are 
members  of  the  finance  committee ; therefore  no  members  of  the 
library  committee  are  members  of  the  executive  committee. 

13.  Given  the  major  premise,  If  the  game  is  lost,  we  lose  the  cham- 
pionship. What  follows  as  the  result  of  the  several  minor  premises  ? 

(а)  The  game  is  lost. 

(б)  The  game  is  won. 

(c)  The  championship  is  lost. 

(d)  The  championship  is  won. 

14.  Given,  x,  y,  z,  P,  Q , R,  so  that 

(a)  Of  x,  y,  z,  one  and  only  one  is  true. 

(5)  Of  P,  Q,  R,  one  and  only  one  is  true. 

(c)  If  x is  true,  P is  true. 

(d)  H y is  true,  Q is  true. 

(e)  If  z is  true,  R is  true. 

Prove,  If  x is  false,  P is  false. 

If  y is  false,  Q is  false. 

If  z is  false,  R is  false. 

— Keynes's  Logic. 

15.  I am  sure  that  he  must  have  known  of  the  plan  ; for  only 
members  of  the  committee  knew  of  it,  and  he  was  a member  of  the 
committee. 

16.  A certain  man  will  make  an  excellent  electrical  engineer  ; for 
he  is  a good  mathematician. 

17.  If  he  insists  upon  the  present  policy,  he  will  fail ; but  he  is 
willing  to  give  up  this  policy  and  therefore  he  will  succeed. 


LOGICAL  EXERCISES 


403 


18.  Only  those  messages  which  are  prepaid  will  be  delivered.  This 
message  has  been  prepaid  ; and  therefore  it  will  be  delivered. 

19.  If  a is  b,  c is  d ; if  c is  d,  e is  f;  if  e is/,  g is  h. 

What  inferences  are  possible  if  yon  have  given  that  e is  d ? 

What  inferences,  if  e is  not  / ? 

20.  A is  nearer  than  B ; B is  nearer  than  C ; therefore  A is  nearer 
than  C. 

21.  All  who  were  pledged  voted  for  him. 

A certain  man  was  not  pledged. 

:.  He  did  not  vote  for  him. 

22.  Because  the  poor  who  have  cows  are  the  most  industrious,  the 
way  to  make  them  industrious  is  to  give  them  cows.  — Malthus. 

23.  Governor  McKinley  charges  that  the  democratic  party  believes 
in  taxing  ourselves.  I’m  afraid,  gentlemen,  we  must  admit  this  charge. 
We  stand  disgraced  in  the  eyes  of  mankind  if  we  cannot  and  if  we  do 
not  support  our  own  government.  We  can  throw  that  support  on  other 
people  only  by  beggary  or  by  force.  If  we  use  the  one,  we  are  a pau- 
per nation  ; if  we  use  the  other,  we  are  a pirate  nation.  — Congressman 
William  L.  Wilson  of  West  Virginia. 

24.  If  the  plate  found  had  been  originally  on  the  outside  of  the  ship, 
I should  have  judged  that  there  must  be  green  paint  on  it ; but  I couldn’t 
find  green  paint  on  that  part  of  the  plate.  — Maine  Court  of  Inquiry. 

25.  Question  : Can  you  imagine  a 10-inch  charge  bursting  inside  of 
a tank  ? Would  they  look  like  that  ? [Showing  a split  tank.] 

Answer : If  a 10-inch  charge  burst  inside  of  a tank,  there  would  be 
nothing  left  of  the  tank.  It  would  be  blown  into  small  pieces. 

26.  No  one  of  the  crowd  would  by  himself  stoop  to  so  mean  an  act, 
and,  therefore,  I am  quite  sure  that  as  a body  they  would  not  do  it. 

27.  Our  rule  in  the  Philippines  is  unjust ; for  it  is  manifestly  unjust 
to  tyrannize  over  an  inferior  people. 

28.  A few  years  ago  there  appeared  an  unusual  number  of  spots  on 
the  sun,  and  there  followed  immediately  a very  severe  famine  in  India. 
It  would  seem  that  such  variations  in  the  nature  of  the  sun  had  some- 
thing to  do  with  the  consequent  failure  of  the  crops. 

29.  There  should  be  no  restriction  of  debate  in  the  United  States 
Senate,  because  freedom  of  speech  is  one  of  our  most  sacred  privileges. 

30.  Each  member  of  a certain  board  is  liable  to  err  in  judgment, 
therefore  as  a body  the  chance  of  error  is  multiplied,  and  consequently 
is  so  much  the  greater. 

31.  It  would  be  greatly  to  our  advantage  as  a people  were  we  to 
have  a silver  standard,  for  the  prosperity  of  the  people  would  be 
increased. 


404 


LOGICAL  EXERCISES 


32.  The  expedition  was  destined  to  fail,  because  it  started  on 
Friday. 

33.  These  men  are  traitors  because  they  are  opposed  to  the  war, 
and  opposition  to  the  war  is  an  opposition  to  the  government,  and 
opposition  to  the  government  is  traitorous. 

34.  The  combination  which  has  been  formed  need  not  be  feared,  for 
all  of  its  members  are  exceedingly  weak  and  inexperienced. 

35.  That  writer  must  be  a follower  of  Plato  ; for  all  followers  of 
Plato  are  idealists,  and  he  is  an  idealist. 

36.  The  philosophy  of  Naturalism,  if  regarded  from  the  practical 
side,  is  insufficient;  if  from  the  speculative  side,  it  is  incoherent. 
Therefore  it  fails  to  justify  itself. — Mr.  Balfour  in  Foundations  of 
Belief. 

37.  It  is  possible  to  have  in  thought  the  conception  of  the  most  per- 
fect Being.  This  conception  implies  the  reality  of  such  a Being ; for 
if  the  most  perfect  Being  as  thus  conceived  has  no  real  existence,  then 
it  would  be  possible  to  conceive  of  a still  more  perfect  Being  which 
should  possess  reality,  and  thus  the  former  would  not  be  the  most 
perfect  Being  possible.  — Anselm's  Ontological  Argument. 

38.  Students  who  are  free  to  choose  their  studies  will,  as  a rule, 
select  the  easiest ; therefore  the  easiest  courses  will  be  largely  attended, 
or,  conversely,  the  much-chosen  courses  will  include  all  the  easiest. 

39.  If  there  had  been  no  portent  of  the  Wilson-Gorman  bill,  there 
would  have  been  no  panic  in  1893,  no  consequent  revenue  deficit,  no 
need  to  issue  bonds  in  time  of  peace,  no  addition  to  the  national  debt, 
no  resulting  16-to-l  free  silver  craze,  and  no  chance  for  the  ring  of 
silver  Senators  to  bestride  the  financial  legislation  of  the  country. 

40.  The  following  is  an  excerpt  from  a letter  written  to  one  of  our 
daily  journals : — 

I am  in  favor  of  free  silver.  First  — Because  I believe  it  to  be  right. 

Second  — Because  it  is  constitutional  and  democratic,  and  right  here 
I may  say  that  for  thirty-two  years  I have  voted  the  democratic 
ticket. 

Washington  and  Jefferson  (the  father  of  Democracy)  bequeathed 
to  the  American  people  in  1792  the  legacy  that  the  dollar  of  371^  grains 
of  pure  silver  was  the  unit  of  value.  This  legacy  was  ever  kept  sacred 
and  preserved  until  1873,  when  Congress  destroyed  the  unit  of  value 
that  had  stood  the  test  for  over  eighty  years  of  American  independence, 
and  substituted  a unit  that  seems  to  be  acceptable  to  the  Rothschilds 
of  England  and  America. 

From  the  effects  of  that  outrage,  the  work,  no  doubt,  of  men  who 
did  not  fully  understand  what  they  were  doing,  the  people  have  never 


LOGICAL  EXERCISES 


405 


recovered.  They  can  still  see  its  effects  by  comparing  the  reduction 
in  value  of  all  property  during  recent  years  with  the  steady  increase 
in  value  which  took  place  before  silver  was  demonetized. 

The  value  of  nearly  everything  that  a man  owned  was  depreciated 
by  the  demonetization  of  silver,  but  then  there  was  no  depreciation  in 
any  debt  that  he  owed ; on  the  contrary  his  debts  increased  because 
gold  appreciated  when  made  the  only  redemption  money  of  the  country, 
and  consequently  it  took  more  labor  and  products  to  get  the  gold  with 
which  to  pay  his  debts. 

The  people  can  also  see  the  effects  of  the  demonetization  of  silver 
by  comparing  the  number  of  strikes  and  lockouts  we  have  had  since 
1873  with  the  number  we  had  for  eighty  years  before.  They  can  see 
its  effect  by  comparing  the  number  of  trusts  of  the  last  fifteen  years 
with  the  number  we  had  before  silver  was  demonetized.  Before  1873 
labor  had  little  cause  to  organize  for  protection.  America  was  the 
asylum  for  the  oppressed  of  all  nations,  and  American  labor  was  the 
best  paid  and  the  most  contented  in  the  world.  How  is  it  now,  and 
how  has  it  been,  on  the  average,  since  the  old  American  policy  of 
“live  and  let  live”  was  abandoned  at  the  behest  of  the  comparative 
few  who  control  the  gold  of  the  world  ? Instead  of  being  those  to 
whom  the  oppressed  of  other  nations  come  for  “fair  play,”  we  are  a 
part  of  the  world’s  great  throng  which  is  trying  to  get  “ fair  play  ” for 
themselves. 

The  masses  of  our  country  are  little,  if  any,  better  off,  all  things 
considered,  than  those  of  the  most  favored  of  the  over-populated 
countries  of  the  old  world.  It  was  not  always  thus,  and  it  will  not 
long  continue  to  be  so  if  the  voters  will  turn  a deaf  ear  to  the  pluto- 
crats and  their  agents,  the  time-serving  politicians,  who  tell  them  that 
silver  money  would  be  “dishonest”  money  unless  measured  by  the 
gold  standard  which  these  same  plutocrats  have  substituted  for  the  old 
gold  and  silver  standard  which  we  used  until  1873. 

41.  Luxurious  expenditure  is  a good  thing  for  laborers,  as  it  in- 
creases the  demand  for  labor, 

42.  Payment  of  interest  on  a public  debt,  so  far  as  it  is  confined 
to  the  citizens  of  one  country,  neither  enriches  nor  impoverishes  the 
country,  but  is  a payment  of  money  from  the  right  hand  to  the  left. 

43.  A great  fire  tends  to  increase  wages,  as  it  creates  employment 
to  replace  the  devastated  district. 

44.  A dense  population  implies  a high  rate  of  natural  increase  ; 
hence  (apart  from  immigration)  the  birth-rate  in  a city  is  higher  than 
in  the  country. 

45.  As  a thing  is  generally  sold  for  more  than  it  is  worth,  or  for 


406 


LOGICAL  EXERCISES 


less,  one  of  the  parties  to  an  exchange  commonly  is  a loser  by  the 
transaction. 

46.  An  increase  in  the  amount  of  money  tends  to  lower  the  rate  of 
interest,  for  interest  is  paid  for  the  use  of  money. 

47.  Exchange  between  two  traders  in  the  same  community  com- 
monly results  in  a profit  to  both.  Such  exchange  is  preferable  to 
exchange  where  one  of  the  parties  is  an  outsider,  because  only  one 
profit  is  realized  by  the  community  in  the  latter  case. 

48.  The  two  following  syllogisms  are  after  the  Stoic  manner : — 

(a)  Nihil  est  tam  contra  naturam  quam  turpitudo. 

Nihil  est  tam  secundum  naturam  quam  utilitas. 

. \ In  eadem  re  utilitas  et  turpitudo  esse  non  possunt. 

(f>)  Quod  honestum  est,  id  est  aut  solum  aut  summum  bonum. 

Quod  autem  bonum  est  id  certe  utile. 

Itaque,  quidquid  honestum,  id  utile. 

— Cicero,  De  Officiis,  III.  viii , 35. 

49.  There  is  no  such  thing  as  innate  knowledge.  As  it  is  evident 
that  new-born  children,  idiots,  and  even  the  great  part  of  illiterate 
men  have  not  the  least  apprehension  of  the  axioms  alleged  to  be  innate, 
the  advocates  of  innate  ideas  are  obliged  to  assume  that  the  mind  can 
have  ideas  without  being  conscious  of  them.  But  to  say  a notion  is 
imprinted  on  the  mind  and  at  the  same  time  to  maintain  that  the 
mind  is  ignorant  of  it,  is  to  make  this  impression  nothing.  If  the 
words,  to  be  in  the  understanding,  have  any  positive  meaning,  they 
signify  to  be  perceived  and  to  be  understood  by  the  understanding: 
hence,  if  any  one  asserts  that  a thing  is  in  the  understanding  and  yet 
not  understood  by  the  understanding,  and  that  it  is  in  the  mind  with- 
out being  perceived  by  the  mind,  it  amounts  to  saying  that  a thing  is 
and  is  not  in  the  understanding.  — Locke,  Essay  on  Human  Under- 
standing. 

50.  There  are  some  philosophers  who  imagine  we  are  every  mo- 
ment intimately  conscious  of  what  we  call  our  Self ; that  we  feel  its 
existence  and  its  continuance  in  existence  ; and  are  certain,  beyond  the 
evidence  of  a demonstration,  both  of  its  perfect  identity  and  simplicity. 
Now,  it  is  evident  that  there  must  be  some  one  impression  that  gives 
rise  to  every  real  idea.  But  self  or  person  is  not  any  one  impression, 
but  that  to  which  our  several  impressions  and  ideas  are  supposed  to 
have  a reference.  If  any  impression  gives  rise  to  the  idea  of  self,  that 
impression  must  continue  invariably  the  same  through  the  whole 
course  of  our  lives  ; since  self  is  supposed  to  exist  after  that  manner. 
But  there  is  no  impression  constant  and  invariable.  Pain  and  pleasure, 


LOGICAL  EXERCISES 


407 


grief  and  joy,  passions  and  sensations  succeed  each  other  and  never 
all  exist  at  the  same  time.  It  cannot,  therefore,  be  from  any  of  these 
impressions  or  from  any  other  that  the  idea  of  self  is  derived  ; and 
consequently  there  is  no  such  idea.  — Hume , A Treatise  on  Human 
Nature. 

51.  According  to  the  common  view  external  objects — tables,  trees, 
horses,  dogs  — have  an  existence  quite  independent  of  the  mind  which 
perceives  them,  and  our  ideas  of  them  are  copies  or  resemblances  of 
these  things  without  us.  Berkeley,  however,  combats  this  view  with  the 
following  argument : Either  those  external  objects  or  originals  of  our 
ideas  are  perceivable  or  they  are  not  perceivable.  If  they  are,  then 
they  are  ideas  and  we  have  gained  our  point ; but  if  you  say  they  are 
not,  I appeal  to  any  one  whether  it  be  sense  to  assert  a color  is  like 
something  which  is  invisible  ; hard  or  soft  like  something  intangible; 
and  so  of  the  rest.  — Principles  of  Human  Knowledge. 

52.  Motives  are  good  or  bad  only  on  account  of  their  effects  ; good 
on  account  of  their  tendency  to  produce  pleasure,  or  avert  pain  ; bad 
on  account  of  their  tendency  to  produce  pain  or  avert  pleasure.  Let  a 
man’s  motive  be  ill-will, — call  it  even  malice,  envy,  cruelty,  — it  is  still 
a kind  of  pleasure  that  is  his  motive ; the  pleasure  he  takes  at  the 
thought  of  the  pain  which  he  sees,  or  expects  to  see,  his  adversary 
undergo.  Now  even  this  wretched  pleasure,  taken  by  itself,  is  good  : 
it  may  be  faint ; it  may  be  short ; it  must  at  any  rate  be  impure  ; yet 
while  it  lasts  and  before  any  bad  consequences  arrive,  it  is  as  good  as 
any  other  that  is  not  more  intense.  — Bentham,  Principles  of  Morals 
and  Legislation. 

53.  It  is  in  accordance  with  the  traditional  policy  of  the  United 
States  that  we  should  possess  and  develop  colonies;  for  the  states 
were  themselves  originally  a group  of  colonies,  and  our  territories  have 
always  been  a most  important  feature  of  the  growing  power  of  the 
nation,  and  territory  is  only  another  name  for  colony. 

54.  All  that  we  know  or  conceive  are  our  own  ideas.  When,  there- 
fore, you  say  all  ideas  are  occasioned  by  impressions  in  the  brain,  do 
you  conceive  this  brain  or  no  ? If  you  do,  then  you  talk  of  ideas 
imprinted  in  an  idea  causing  that  same  idea,  which  is  absurd.  If  you 
do  not  conceive  it,  you  talk  unintelligibly,  instead  of  forming  a rea- 
sonable hypothesis.  — Berkeley,  Hylas  and  Pliilonous. 

65.  What  proves  the  soul  to  be  matter  — exceedingly  fine  matter, 
of  course  — is  the  influence  exercised  upon  it  by  the  body  in  fainting, 
anaesthesia,  and  delirium,  in  cases  of  injury  and  disease,  and,  above 
all,  the  fact  that  the  advance  and  the  decline  of  the  soul  correspond 
to  analogous  bodily  conditions.  The  intellectual  faculties  are  weak  in 


408 


LOGICAL  EXERCISES 


the  period  of  childhood  ; they  grow  strong  in  youth,  and  gradually 
decay  in  old  age.  Sickness  causes  a serious  reaction  upon  the  soul ; 
without  the  body  the  soul  has  no  power  to  manifest  itself.  Nay,  more 
than  that,  the  dying  man  does  not  feel  his  soul  gradually  withdrawing 
from  one  organ  to  another,  and  then  finally  making  its  escape  with  its 
powers  unimpaired  ; he  experiences  a gradual  diminution  of  his  mental 
faculties.  — Epicurus. 

56.  Consequens  est : Si  orator  est,  homo  est.  Inconsequens  est : 
Si  homo  est,  orator  est.  Repugnans : Si  homo  est,  quadrupes  est. 

— Augustine,  Be  Boot.  Christ.,  II,  34. 

57.  The  Greeks  honored  the  gods  and  also  the  actors  who  took 
part  in  scenic  games  (often  debasing)  in  honor  of  the  gods.  The 
Romans  excluded  such  actors  from  citizenship  on  the  ground  that 
their  calling  was  degrading.  Augustine  reasons  as  follows  : — 

Proponunt  Graeci : Si  tales  dii  colendi  sunt,  tales  homines  hono- 
randi.  Adsumunt  Romani : Sed  nullo  modo  tales  homines  honorandi 
sunt.  Concludunt  Christiani:  Nullo  modo  igitur  dii  tales  colendi 
sunt. — Be  Civ.  Bei,  II,  13. 

58.  Bain,  in  Senses  and  Intellect  (p.  374),  argues  that  “the  con- 
joint experience  of  the  senses  and  the  movements  appears  to  me  to 
furnish  all  that  we  possess  in  the  notion  of  extended  matter.  The 
association  between  sight  and  locomotion,  or  between  touch  and  the 
movements  of  the  arm,  tells  us  that  a given  appearance  implies  the 
possibility  of  a certain  movement ; that  a remote  building  implies  a 
continuance  of  our  walking  exertions  to  change  its  appearance  into 
another  that  we  call  a near  view ; and  the  power  of  moving,  the  scope 
for  moving,  exhausts  every  property  in  the  idea  of  empty  space.  We 
estimate  it  first  by  our  own  movements,  and  next  by  other  movements 
measured  in  the  first  instance  by  our  own,  as,  for  example,  the  flight 
of  a bird,  the  speed  of  a cannon  ball,  or  the  movement  of  light.  The 
mental  conception  that  we  have  of  empty  space  is  scope  for  movement.” 

Professor  Baldwin,  in  the  Handbook  of  Psychology  (Vol.  I,  p.  136), 
criticises  the  above  as  follows:  “Now,  if  the  idea  of  space  enters 
through  the  intensive  feeling  of  muscular  contraction,  there  is  more 
in  our  conclusion  than  in  our  premises,  and  we  have  an  ignoratio  ; if, 
on  the  other  hand,  the  sensation  is  one  of  movement  proper,  extension 
has  already  entered  and  we  need  no  association  ; this  is  a petitio." 

59.  In  mediaeval  times  it  was  held  that  Venus  or  that  Saturn  was 
inhabited,  not  because  any  one  could  devise,  with  any  degree  of  proba- 
bility, any  organized  structure  which  would  be  suitable  for  animal 
existence  on  the  surfaces  of  those  planets,  but  because  it  was  conceived 
that  the  greatness  or  goodness  of  the  Creator,  or  His  wisdom,  or  some 


LOGICAL  EXERCISES 


409 


other  of  His  attributes,  would  be  manifestly  imperfect  if  these  planets 
were  not  tenanted  by  living  creatures.  — Whewell. 

60.  That  God  is,  the  Bible  affirms.  Whatever  the  Bible  affirms  is 
true,  because  it  is  from  God,  and  declares  it  is  impossible  for  God  to 
lie.  Therefore  the  existence  of  God  is  surely  proved. 

61.  No  species  of  agnosticism  is  unrelated  to  its  genus.  No  agnos- 
ticism with  a special  reference  or  limited  sphere  is  without  reference 
to  the  agnostic  idea,  spirit,  and  aim.  On  the  contrary,  every  kind  of 
agnosticism  tends  towards  agnostic  completeness.  Agnosticism  in  any 
form  is  of  the  nature  of  agnosticism  in  every  form.  — Flint,  Agnos- 
ticism, p.  311. 

62.  The  propounders  of  what  are  called  the  “ethics  of  evolution” 
adduce  a number  of  more  or  less  interesting  facts,  and  more  or  less 
sound  arguments  in  favor  of  the  origin  of  the  moral  sentiments  in  the 
same  way  as  other  natural  phenomena,  by  a process  of  evolution.  I 
have  little  doubt,  for  my  own  part,  that  they  are  on  the  right  track  ; 
but  as  the  immoral  sentiments  have  been  no  less  evolved,  there  is,  so 
far,  as  much  natural  sanction  for  the  one  as  the  other.  The  thief  and 
the  murderer  follow  nature  just  as  much  as  the  philanthropist. — 
Huxley,  Evolution  and  Ethics. 

63.  There  is  another  fallacy  wdiich  appears  to  me  to  pervade  the 
so-called  “ ethics  of  evolution.”  It  is  the  notion  that  because,  on  the 
whole,  animals  and  plants  have  advanced  in  perfection  of  organization 
by  means  of  the  struggle  for  existence  and  the  consequent  survival  of 
the  fittest ; therefore  men  in  society,  men  as  ethical  beings,  must  look 
to  the  same  process  to  help  them  towards  perfection.  - — Huxley. 

64.  A profound  study  of  the  system  of  protection  has  taught  us  this 
syllogism,  upon  which  the  whole  doctrine  reposes  : — 

The  more  men  work  the  richer  they  become  ; 

The  more  difficulties  there  are  to  be  overcome,  the  more  work  ; 

Ergo , The  more  difficulties  there  are  to  be  overcome,  the  richer 
they  become.  — Bastiat,  Economic  Sopthisms. 

65.  The  shopkeeper  thrives  only  by  the  irregularities  of  youth  ; the 
farmer  by  the  high  prices  of  corn  ; the  architect  by  the  destruction  of 
houses  ; the  officers  of  justice  by  lawsuits  and  quarrels.  Ministers  of 
religion  derive  their  distinction  and  employment  from  our  vices  and 
our  death.  No  physician  rejoices  in  the  health  of  his  friends,  nor 
soldiers  in  the  peace  of  his  country  ; and  so  of  the  rest.  Therefore 
carelessness,  calamity,  pestilence,  disease,  and  even  death  are  economic 
blessings.  — Montaigne. 

66.  Restrictive  laws  always  land  us  in  this  dilemma  : Either  you 
admit  that  they  produce  scarcity,  or  you  do  not.  If  you  admit  it,  you 


410 


LOGICAL  EXERCISES 


avow  by  the  admission  that  you  inflict  on  the  people  all  the  injury  in 
your  power.  If  you  do  not  admit  it,  you  deny  having  restricted  the 
supply  and  raised  prices,  and  consequently  you  deny  having  favored 
the  producer. — Basticit. 

67.  When  products  such  as  coal,  iron,  corn,  or  textile  fabrics  are 
sent  us  from  abroad,  and  we  can  acquire  them  with  less  labor  than  if 
we  made  them  ourselves,  the  difference  is  a free  gift  conferred  upon 
us.  The  gift  is  more  or  less  considerable  in  proportion  as  the  differ- 
ence is  more  or  less  great.  It  amounts  to  a quarter,  a half,  or  three- 
quarters  of  the  value  of  the  product  when  the  foreigner  only  asks  us 
for  three-fourths,  a half,  or  a quarter  of  the  price  we  should  otherwise 
pay.  It  is  as  perfect  and  complete  as  it  can  be,  when  the  donor  (like 
the  sun  in  furnishing  us  with  light)  asks  us  for  nothing.  The  question, 
and  we  ask  it  formally,  is  this : Do  you  desire  for  our  country  the 
benefit  of  gratuitous  consumption,  or  the  pretended  advantages  of 
onerous  production  ? Make  your  choice,  but  be  logical ; for  as  long  as 
you  exclude  as  you  do,  coal,  iron,  corn,  foreign  fabrics  in  proportion 
as  their  price  approximates  to  zero,  what  inconsistency  would  it  be  to 
admit  the  light  of  the  sun,  the  price  of  which  is  already  at  zero  during 
the  entire  day  ? — Bastiat. 

68.  To  hear  the  roaring  of  the  sea  as  one  does,  one  must  hear  the 
parts  which  compose  its  totality,  that  is,  the  sound  of  each  wave,  . . . 
although  this  noise  would  not  be  noticed  if  the  wave  were  alone.  One 
must  be  affected  a little  by  the  movement  of  one  wave,  one  must  have 
some  perception  of  each  several  noise,  however  small  it  be.  Otherwise 
one  would  not  hear  that  of  100,000  waves,  for  of  100,000  zeros  one  can 
never  make  a quantity.  — Leibniz. 

69.  Mr.  Spencer,  in  his  exposition  of  the  doctrine  of  evolution,  is 
guilty  of  the  amazing  fallacy  of  supposing  that,  because  the  laws  of 
energy  are  everywhere  present,  they  are  everywhere  sufficient  to  ex- 
plain what  we  see  ; which  is  much  the  same  as  assuming  that,  because 
a painter’s  palette,  like  his  finished  canvas,  shows  us  a mixture  of 
colors  laid  on  with  a brush,  therefore  what  sufficed  to  produce  the 
one  would  equally  suffice  to  produce  the  other.  — Professor  Ward, 
Naturalism  and  Agnosticism. 

70.  No  one  can  believe  what  he  does  not  understand ; therefore 
there  are  no  mysteries  in  true  religion. 

71.  Christianity  is  necessarily  modified  by  the  growth  of  civilization 
and  the  exigencies  of  the  times ; therefore  the  Catholic  priesthood, 
though  necessary  in  the  Middle  Ages,  may  be  superseded  now. 

72.  There  are  rights  of  conscience  such  that  every  one  may  lawfully 
advance  a claim  to  profess  and  teach  what  is  false  and  wrong  in  mat- 


LOGICAL  EXERCISES 


411 


ters  religious,  social,  and  moral,  provided  that  it  seems  absolutely 
true  and  right  to  his  private  conscience  ; therefore  individuals  have  a 
right  to  preach  and  practise  polygamy. 

73.  There  is  no  such  thing  as  a national  or  state  conscience ; 
therefore  no  judgments  can  fall  upon  a sinful  nation. 

74.  The  civil  power  lias  no  positive  duty  in  a normal  state  of 
things  to  maintain  religious  truth  ; therefore  blasphemy  and  Sabbath- 
breaking are  not  rightly  punishable  by  law. 

75.  The  civil  power  may  dispose  of  church  property  without  sacri- 
lege ; therefore  Henry  VIII  committed  no  sin  in  his  spoliations. 

76.  The  civil  power  has  the  right  of  ecclesiastical  jurisdiction  and 
administration ; therefore  parliament  may  impose  articles  of  faith  on 
the  church  or  suppress  dioceses. 

77.  The  people  are  the  legitimate  source  of  power ; therefore  uni- 
versal suffrage  is  among  the  natural  rights  of  man. 

78.  Virtue  is  the  child  of  knowledge  and  vice  of  ignorance ; there- 
fore education,  periodical  literature,  travelling,  ventilation,  drainage, 
and  the  arts  of  life,  when  fully  carried  out,  serve  to  make  a population 
moral  and  happy. 

79.  Unbelievers  use  the  antecedent  argument  from  the  order  of 
nature  against  our  belief  in  miracles.  Here,  if  they  only  mean  that 
the  fact  of  that  system  of  laws,  by  which  physical  nature  is  governed, 
makes  it  antecedently  improbable  that  an  exception  should  occur  in  it, 
there  is  no  objection  to  the  argument ; but  if,  as  is  not  uncommon, 
they  mean  that  the  fact  of  an  established  order  is  fatal  to  the  very 
notion  of  an  exception,  they  are  using  a presumption  as  if  it  were  a 
proof.  — Newman,  Grammar  of  AsseMf. 

80.  Gibbon  mentions  five  causes  to  account  for  the  establishment  of 
Christianity, — the  zeal  of  the  Christians,  inherited  from  the  Jews, 
their  doctrine  of  a future  state,  their  claim  to  miraculous  power,  their 
virtues,  and  their  ecclesiastical  organization.  He  thinks  these  five 
causes,  when  combined,  will  fairly  account  for  the  event ; but  he  has 
not  thought  of  accounting  for  their  combination.  If  they  are  ever  so 
available  for  his  purpose,  still  that  availableness  arises  out  of  their 
coincidence,  and  out  of  what  does  that  coincidence  arise  ? — Newman. 

81.  Bentham  was  clearly  the  victim  of  a common  delusion.  If  a 
system  will  work,  the  minutest  details  can  be  exhibited.  Therefore, 
it  is  inferred,  an  exhibition  of  minute  detail  proves  that  it  will  work. 
Unfortunately,  the  philosophers  of  Laputa  would  have  had  no  more 
difficulty  in  filling  up  details  than  the  legislators  of  England  or  the 
United  States.  — Leslie  Stephen , The  English  Utilitarians. 

82.  The  “ rights  of  man  ” doctrine  confounds  a primary  logical  canon 


412 


LOGICAL  EXERCISES 


with  a statement  of  fact.  Every  political  theory  must  be  based  upon 
facts  as  well  as  upon  logic.  Any  reasonable  theory  about  politics  must 
no  doubt  give  a reason  for  inequality  and  a reason,  too,  for  equality. 
The  maxim  that  all  men  were  or  ought  to  be  “ equal  ” asserts  correctly 
that  there  must  not  be  arbitrary  differences.  Every  inequality  should 
have  its  justification  in  a reasonable  system.  But  when  this  undeni- 
able logical  canon  is  taken  to  prove  that  men  actually  are  equal,  there 
is  an  obvious  begging  of  the  question.  —Leslie  Stephen. 

83.  I shall  offer  this  one  mark  whereby  prejudice  may  be  known. 
He  that  is  strongly  of  any  opinion  must  suppose  (unless  he  be  self- 
condemned)  that  his  persuasion  is  built  upon  good  grounds,  and  that 
his  assent  is  no  greater  than  what  the  evidence  of  the  truth  he  holds 
forces  him  to ; and  that  they  are  arguments  and  not  inclinations  of 
fancy  that  make  him  so  confident  and  positive  in  his  tenets.  Now  if, 
after  all  his  profession,  he  cannot  bear  any  opposition  to  his  opinion  — 
if  he  cannot  so  much  as  give  a patient  hearing,  much  less  examine  and 
weigh  the  arguments  on  the  other  side  — does  he  not  plainly  confess,  it 
is  prejudice  governs  him  ? And  it  is  not  the  evidence  of  truth,  but 
some  lazy  anticipation,  some  beloved  presumption  that  he  desires  to 
rest  undisturbed  in.  For,  if  what  he  holds  be  as  he  gives  out,  well 
fenced  with  evidence,  and  he  sees  it  to  be  true,  what  need  he  fear  to 
put  it  to  the  proof  ? — Locke , The  Conduct  of  the  Understanding. 

84.  When  Mill  urges  us  to  choose  the  higher  rather  than  the  lower 
pleasures,  then  either  the  so-called  “higher”  pleasure  is  actually,  as 
pleasure,  so  preferable  to  that  called  “ lower  ” that  the  smaller  amount 
of  the  one  would  be  more  pleasurable  than  the  largest  amount  of  the 
other ; or  else  the  higher  is  called  higher  and  is  to  be  preferred  to  the 
lower  — even  though  the  latter  may  be  greater  as  pleasure — because 
of  a quality  belonging  to  it  over  and  above  its  character  as  pleasant 
feeling.  The  former  verdict  would  be,  in  the  first  place,  paradoxical, 
and  in  the  second  place  would  give  up  Mill’s  case  by  reducing  quality 
to  a quantitative  standard.  According  to  the  latter  verdict,  the  char- 
acteristic upon  which  the  distinction  of  quality  depends,  and  not 
pleasure  itself,  becomes  the  ethical  standard.  — Sorley,  Ethics  of 
Naturalism. 

85.  Every  one  desires  happiness;  virtue  is  happiness;  therefore 
every  one  desires  virtue.  — Aristotle. 

86.  The  principles  of  justice  are  variable ; the  appointments  of 
nature  are  invariable  ; therefore  the  principles  of  justice  are  no 
appointment  of  nature.  — Aristotle. 

87.  It  is  no  doubt  true  that  if  a law  be  universal,  it  will  be  confirmed 
by  all  our  experiments ; therefore,  when  all  our  experiments  fail  to 
detect  an  exception,  we  may  regard  the  law  as  true  universally. 


LOGICAL  EXERCISES 


413 


PART  II 

1.  When  a coin  and  a feather  are  dropped  simultaneously  in  the 
receiver  of  an  air-pump,  the  air  being  left  in,  the  feather  flutters  to 
the  bottom  after  the  coin ; but,  when  the  air  is  pumped  out  of  the 
receiver,  the  coin  and  the  feather,  being  dropped  at  the  same  instant, 
reach  the  bottom  of  the  receiver  together. 

2.  If  a beam  of  the  sun’s  light  is  passed  through  a prism,  a colored 
band  nearly  five  times  as  long  as  it  is  broad  results.  Newton  tried 
several  experiments  in  which  he  varied  the  size  of  prism,  and  the 
quality  of  the  glass  ; he  also  passed  the  beam  through  various  parts  of 
the  same  prism,  and  tried  other  minor  suppositions.  But  in  all  these 
cases  there  was  the  same  color  effect  produced. 

3.  Nitrogen  obtained  from  various  chemical  sources  is  of  uniform 
density  ; in  1894,  Lord  Rayleigh  and  Professor  Ramsay,  noting  the 
fact  that  atmospheric  nitrogen  is  about  one-half  per  cent  heavier,  were 
led  to  the  discovery  of  a hitherto  unknown  substance  which  received 
the  name  of  argon. 

4.  If  the  earth  were  9500  miles  in  diameter  instead  of  8000,  this 
increase  would  give  two-thirds  increase  in  bulk,  and  a corresponding 
increase  of  density  due  to  the  greater  gravitative  force  ; the  mass 
would  be  about  double  what  it  is.  But  with  double  the  mass,  the 
quantity  of  gases  of  all  sorts  attracted  and  retained  by  gravity  would 
probably  have  been  double,  and  in  that  case  there  would  have  been 
double  the  quantity  of  water  produced,  as  no  hydrogen  would  then 
escape.  But  the  surface  of  the  globe  would  be  only  one-half  greater 
than  at  present,  in  which  case  the  water  would  have  sufficed  to  cover 
the  whole  surface  several  miles  deep. 

5.  Wherever  the  winds  blow  over  extensive  areas  of  water  on  to 
the  land,  especially  if  there  are  mountains  or  elevated  plateaus  which 
cause  the  moisture-laden  air  to  rise  to  heights  where  the  temperature 
is  lower,  clouds  are  formed  and  rain  falls.  But  where  the  land  is  of 
an  arid  nature  and  much  heated  by  the  sun,  the  air  becomes  capable 
of  holding  still  more  aqueous  vapor,  and  even  dense  rain-clouds  disperse 
without  producing  any  rainfall. 

6.  Very  thin  sheets  of  white  light  proceeding  from  various  incan- 
descent substances  are  passed  through  incandescent  hydrogen,  and 
the  emergent  light  is  then  separated  into  its  constituent  elements  by  a 
prism.  In  the  spectra  thus  obtained  it  is  found  that  there  are  invariably 
dark  lines  occupying  precisely  the  same  relative  position.  But  trying 
similar  experiments  with  any  other  element  than  incandescent  hydro- 


414 


LOGICAL  EXERCISES 


gen,  the  lines  obtained  never  occupy  the  same  positions  in  the  spectrum 
as  the  lines  in  question. 

7.  (a)  Hawksbee  in  1715  first  noticed  that  by  striking  a bell  in  the 
receiver  of  an  air-pump,  the  bell  was  heard  when  the  receiver  was  full 
of  air  ; but  when  the  receiver  was  exhausted,  no  sound  was  heard. 

(6)  Also,  it  was  found  that  as  the  air  was  gradually  admitted  into 
the  receiver,  the  sound  of  the  bell  grew  louder  and  louder. 

8.  The  following  are  the  results  of  a series  of  experiments  conducted 
by  Dr.  Wells  in  order  to  discover  the  cause  of  dew  : — 

(a)  Moisture  bedews  a cold  metal  or  stone  when  we  breathe  upon  it. 
The  same  appears  on  a glass  of  ice-water,  and  on  the  inside  of  windows 
when  sudden  rain  or  hail  chills  the  external  air  ; the  inference  is  that 
when  an  object  contracts  dew,  it  is  colder  than  the  surrounding  air. 

(b)  No  dew  is  deposited  on  a piece  of  metal  which  has  been  polished, 
but  on  the  same  metal  unpolished  dew  is  deposited  copiously.  There- 
fore the  deposit  of  dew  is  affected  by  the  kind  of  surface  which  is 
exposed. 

(c)  With  various  kinds  of  polished  metals,  no  dew  is  deposited  ; 
but  with  various  kinds  of  glass,  having  highly  polished  surfaces,  dew 
is  deposited.  Therefore,  the  deposit  of  dew  is  affected  also  by  the 
kind  of  substances  themselves. 

(d)  In  general,  it  has  been  found  that  those  substances  are  most 
strongly  dewed  which  conduct  heat  worst,  while  those  which  conduct 
heat  well  resist  dew  most  effectively. 

(e)  Again,  substances  of  close  firm  texture,  as  stones  and  metals, 
have  less  dew,  while  substances  of  looser  texture,  as  cloth,  wool,  velvet, 
eider-down,  cotton,  have  more  dew.  But  substances  of  loose  texture 
resist  the  passage  of  heat,  therefore  the  more  these  substances  resist 
the  passage  of  heat  the  greater  the  deposit  of  dew. 

(/)  All  instances  in  which  much  dew  is  deposited  have  this  feature 
in  common  : they  either  radiate  heat  rapidly  or  conduct  it  slowly. 
All  instances  in  which  no  dew  or  very  little  is  deposited  have  in  com- 
mon the  opposite  feature. 

(ff)  The  property  of  radiating  heat  rapidly,  or  conducting  it  slowly, 
signifies  that  the  body  in  question  tends  to  lose  heat  more  rapidly  from 
the  surface  than  it  can  be  restored  from  within.  And  this  in  turn 
renders  the  body  colder  than  the  surrounding  air.  Therefore  a body 
colder  than  the  surrounding  air  precipitates  the  dew  upon  it. 

(fi)  It  is  known  by  direct  experiment  that  for  any  given  degree  of 
temperature,  only  a limited  quantity  of  water  can  remain  suspended 
in  the  state  of  vapor,  and  this  quantity  grows  less  and  less  as  the 
temperature  diminishes.  Therefore  if  there  is  already  as  much  vapor 


LOGICAL  EXERCISES 


415 


suspended  as  the  air  will  contain  at  its  existing  temperature,  any 
lowering  of  the  temperature  will  cause  necessarily  a portion  of  the 
vapor  to  he  condensed  and  become  water. 

(i)  It  is  possible  by  cooling  the  surface  of  any  body  to  find  some 
temperature  lower  than  that  of  the  surrounding  air,  at  which  the  dew 
begins  to  appear. 

( j)  It  is  observed  that  dew  is  not  deposited  on  cloudy  nights,  but 
if  the  clouds  withdraw  and  leave  a clear  opening  a deposition  of  dew 
immediately  begins.  Dew  formed  in  clear  intervals  disappears  when 
the  sky  becomes  thickly  overcast.  Now  a clear  sky  is  nothing  but  the 
absence  of  clouds,  and  it  is  a known  property  of  clouds  that  they  keep 
up  the  temperature  of  exposed  surfaces  by  radiating  heat  to  them. 
We  see  that  the  disappearance  of  clouds  will  cause  these  surfaces  to 
cool,  and  cold  surfaces,  as  has  been  shown,  condense  the  moisture  of 
the  air  in  the  form  of  dew. 

9.  To  the  Editor  of  The  Tribune. 

Sir:  In  your  issue  of  Sunday,  February  7,  is  an  article  entitled 
“Results  of  Antitoxin  Treatment.”  After  quoting  statistics  showing 
a remarkable  decrease  in  the  mortality  from  diphtheria  treated  with 
antitoxin,  as  compared  to  diphtheria  treated  without  antitoxin,  you 
say:  — 

“ The  one  point  now  in  doubt,  and,  it  must  be  confessed,  in  serious 
doubt,  is  the  effect  of  antitoxin  itself  upon  the  human  system.  In 
many  cases  this  has  seemed  to  be  injurious,  if  not  fatal.  Patients  have 
been  cured  of  diphtheria,  only  to  suffer  from  declining  vitality  and  a 
train  of  grievous  disorders  sometimes  baffling  the  physicians’  skill  and 
ending  in  death.  Are  they  caused  by  antitoxin  ? ” 

Before  the  antitoxin  treatment  was  dreamed  of  it  was  a common 
occurrence  — more  common  than  now  — for  a patient  to  be  “ cured  of 
diphtheria”  and  then  to  “suffer  from  declining  vitality,”  etc.,  all  too 
frequently  “ending  in  death.” 

But  no  one  ascribed  these  post-diphtheritic  fatalities  to  the  treat- 
ment. They  were,  very  properly,  believed  to  be  the  result  of  the 
action  of  the  poison  of  diphtheria  upon  the  cells  of  the  body.  There 
can  be  no  doubt  that  this  toxin  (poison)  has  the  power  seriously  to 
affect,  and  even  to  destroy,  certain  tissues.  Therefore  it  is  common 
for  diphtheria  to  be  accompanied  or  followed  by  palsies,  Bright’s  dis- 
ease, neuritis,  anaemia  (declining  vitality),  etc. 

A child  who  has  had  diphtheria  is  liable  to  suffer  from  the  dele- 
terious effects  for  months  or  even  years.  That  these  results  are  due 
to  the  toxin  of  diphtheria  and  not  to  the  antitoxin  is  very  clearly  shown 
by  the  fact  that  the  mortality  and  the  serious  after-effects  are  so  much 


416 


LOGICAL  EXERCISES 


less  when  the  antitoxin  is  used  early  in  the  disease  than  when  it  is  used 
in  the  last  stages  thereof,  i.e.  when  the  antitoxin  is  administered  early 
the  poison  is  destroyed  before  it  has  had  time  to  do  extensive  injury. 

10.  Further  explanation  is  needed  of  the  extraordinary  increase  in 
deaths  from  consumption  in  this  state  as  shown  by  the  annual  report 
of  the  State  Board  of  Health.  There  were  361  more  deaths  by  con- 
sumption reported  in  1899  than  in  1898,  and  the  number  was  419  more 
than  the  average  for  the  preceding  twenty-one  years.  The  increase  in 
deaths  from  acute  lung  diseases  is  also  noteworthy,  and  as  the  same 
conditions  which  give  rise  to  the  latter  are  likely  to  produce  fatal  ter- 
mination in  chronic  cases,  the  connection  between  the  two  is  perhaps 
not  difficult  to  establish.  There  must,  however,  have  been  some  special 
cause  for  the  unusual  mortality  from  diseases  of  the  lungs. 

The  hypothesis  may  be  advanced  that  there  was  no  real  increase 
over  past  years,  but  that  the  apparent  increase  is  due  to  fuller  and 
more  accurate  reports.  This  can  hardly  be  accepted  as  a plausible 
explanation,  since  the  system  of  gathering  mortuary  statistics  last  year 
was  the  same  that  had  been  employed  for  a number  of  years  previously, 
and  is  as  complete  as  can  be  devised  to  secure  accuracy.  The  cause 
must  be  looked  for  elsewhere,  and  it  will  probably  be  found  by  a care- 
ful study  of  the  atmospheric  and  climatic  conditions  existent  during 
the  year  just  ended.  The  winter  was  not  one  of  more  than  ordinary 
severity,  but  attended  with  sudden  and  sharp  variations  of  tempera- 
ture, always  trying  upon  persons  of  weak  lungs.  There  was  much 
snow  and  slush,  filling  the  air  with  moisture,  and  during  the  late  winter 
and  early  spring  dense  fogs  were  frequent.  The  spring  months  were 
also  marked  by  rapid  changes  in  temperature,  while  during  the  summer 
cool  nights  following  hot  days  were  the  rule. 

Considerable  light  might  be  thrown  on  the  matter  by  noting  whether 
the  increase  in  deaths  was  general  throughout  the  state  or  confined  to 
certain  localities  ; whether  there  was  any  difference  between  the  region 
adjacent  to  the  sea-coast  and  the  more  remote  sections,  where  the  influ- 
ence of  the  ocean  upon  the  climate  is  not  so  marked.  The  reports 
from  city  and  country  might  also  be  compared. 

11.  To  the  philosopher  the  state  is  a human  organism,  a human 
person ; but  if  so,  the  human  spirit  which  lives  in  it  must  also  have  a 
human  body,  for  spirit  and  body  belong  to  one  another,  and  between 
them  make  up  the  person.  In  a body  which  is  not  organized  and 
human,  the  spirit  of  man  cannot  truly  live.  The  body  politic  must 
therefore  imitate  the  body  natural  of  man.  The  perfect  state  is,  as  it 
were,  the  visible  body  of  humanity.  — Bluntschli,  Theory  of  the  State. 

12.  In  the  Yale-Princeton  intercollegiate  debate  in  1895,  Yale  con- 


LOGICAL  EXERCISES 


417 


tended  that  the  referendum  had  failed  in  Switzerland,  and  therefore, 
in  all  probability,  would  fail  in  the  United  States.  On  the  other  hand, 
Princeton  maintained  that  the  referendum  had  succeeded  in  Switzer- 
land, and  therefore,  in  all  probability,  would  succeed  in  the  United 
States.  Supposing  the  premise  true  in  each  case,  which  position  is 
the  stronger  ? 

13.  We  may  observe  a very  great  similitude  between  the  earth 
which  we  inhabit  and  the  other  planets.  They  all  revolve  around  the 
sun  as  the  earth  does,  though  at  different  distances  and  in  different 
periods.  They  borrow  all  their  light  from  the  sun  as  the  earth  does. 
Several  of  them  are  known  to  revolve  round  their  axis  like  the  earth, 
and  by  that  means  have  a like  succession  of  day  and  night.  Some  of 
them  have  moons  that  serve  to  give  them  light  in  the  absence  of  the 
sun,  as  our  moon  does  to  us.  They  are  all,  in  their  motions,  subject 
to  the  same  law  of  gravitation  as  the  earth  is.  From  all  this  simili- 
tude, it  is  not  unreasonable  to  think  that  these  planets  may,  like  our 
earth,  be  the  habitation  of  various  orders  of  living  creatures. — Reid, 
Intellectual  Powers. 

14.  Some  remarkable  observations  of  the  French  astronomer, 
M.  Camille  Flaminarion,  have  been  recently  reported,  which  go  to 
show  that  within  certain  limits  the  radiations  of  heat  from  the  sun 
vary  quite  regularly  during  the  eleven  and  a half  year  sun-spot  cycle, 
and  that  these  variations  of  solar  heat  apparently  cause  some  defi- 
nite changes  in  the  natural  phenomena  of  the  earth.  For  instance, 
his  figures  prove  that  when  sun  spots  are  most  numerous  (as  in 
1893),  migratory  birds  return  to  any  given  place  earlier  in  the  year  than 
usual ; and,  on  the  contrary,  when  spots  are  at  a minimum,  they  do 
not  come  back  until  a much  later  date.  These  phenological  researches 
corroborate  previous  evidence,  proving  that  after  the  sun  has  been 
abnormally  agitated  — erupting  enormous  tongues  of  flame  one  hun- 
dred thousand  miles  high,  which  frequently  form  directly  over  the 
spots  — the  earth  receives  more  heat ; and  when  (as  was  the  case  in 
1898)  the  sun  is  comparatively  calm  and  spotless  he  is  less  fiery,  and 
hence  slightly  less  influential  on  our  globe. 

Because  the  well-known  periodic  changes  of  solar  activity  are  not 
followed  by  corresponding  synchronous  changes  in  the  earth’s  atmos- 
phere, many  scientists  deny  that  there  is  any  connection  — forgetting 
that  effects  generally  lag  far  behind  their  causes  and  that  nature  seldom 
accomplishes  her  work  at  a leap.  Professor  Yon  Bezold,  the  German 
meteorologist,  expresses  the  view  generally  accepted  by  astronomers, 
when  he  says:  — 

“It  is  not  inconceivable  if  we  should  find  the  explanation  of  that 


418 


LOGICAL  EXERCISES 


remarkable  periodicity  in  the  temperature  of  whole  zones,  demon- 
strated by  Koeppen  in  1873,  which  without  doubt  indicates  a close 
connection  with  the  processes  on  the  sun’s  surface,  although  the 
irregularities  in  the  times  of  occurrence  of  the  maximum  and  minimum 
temperatures,  amounting  to  years  of  delay  in  certain  zones,  seem  at 
first  sight  to  prove  that  there  is  no  such  connection.” 

15.  If  a small  jet  of  steam  is  sent  into  two  large  glass  receivers, 
one  filled  with  ordinary  air,  the  other  with  air  which  has  been  filtered 
by  passing  through  a thick  layer  of  cotton-wool,  so  as  to  keep  back  all 
particles  of  solid  matter,  the  first  vessel  will  be  instantly  filled  with 
condensed,  cloudy-looking  vapor,  while  in  the  other  vessel  the  air  and 
vapor  will  remain  perfectly  transparent  and  invisible. 

16.  It  is  a very  suggestive  fact  that  most  of  the  stars  belonging  to 
the  Milky  Way  have  spectra  of  the  solar  type,  which  indicates  that 
they  are  of  the  same  general  constitution  as  our  sun,  and  are  also  at 
about  the  same  stage  of  evolution ; and  this  may  well  have  arisen 
from  their  origin  in  a great  nebulous  mass  situated  at  or  near  the 
centre  of  the  galactic  plane,  and  probably  revolving  round  their  com- 
mon centre  of  gravity.  — Wallace,  Man's  Place  in  the  Universe. 

17.  If  the  moon  had  been  destined  to  be  merely  a lamp  to  our 
earth,  there  was  no  occasion  to  variegate  its  surface  with  lofty  moun- 
tains and  extinct  volcanoes,  and  cover  it  with  large  patches  of  matter 
that  reflect  different  quantities  of  light  and  give  its  surface  the  appear- 
ance of  continents  and  seas.  It  would  have  been  a better  lamp  had  it 
been  a smooth  piece  of  lime  or  of  chalk.  It  is  therefore  prepared  for 
inhabitants,  and  similarly  all  other  satellites  are  also  inhabited.  — Sir 
David  Brewster. 

18.  A chemist,  as  Mill  observes,  analyzes  a substance,  and  assum- 
ing the  accuracy  of  his  results,  we  at  once  infer  a general  law  of 
nature  from  “a  single  instance.”  But  if  any  one  from  the  beginning 
of  the  world  has  seen  that  crows  are  black,  and  a single  credible  wit- 
ness says  that  he  has  seen  a gray  crow,  we  abandon  at  once  a conjunc- 
tion which  seemed  to  rest  upon  invariable  and  superabundant  evidence. 
Why  is  a “single  instance”  sufficient  in  one  case,  and  any  number  of 
instances  insufficient  in  the  other  ? 

19.  What  is  the  explanation  of  the  following  quotation  from  Scho- 
penhauer : “False  judgments  are  frequent,  false  conclusions  very 
rare.” 

20.  Stahl,  a contemporary  of  Newton,  supposed  that  all  combust- 
ible substances  contain  a common  element,  or  fire  principle,  which  he 
called  phlogiston,  and  which  escapes  in  the  process  of  combustion. 
But  when  it  was  observed  that  zinc  and  lead  and  sundry  other  sub- 


LOGICAL  EXERCISES 


419 


stances  grow  heavier  in  burning,  it  seemed  hardly  correct  to  suppose 
that  anything  had  escaped  from  these  substances.  To  this  objection 
the  friends  of  the  fire  principle  replied  that  phlogiston  might  weigh 
less  than  nothing,  that  is,  might  be  endowed  with  a positive  property 
of  levity,  so  that  to  subtract  it  from  a body  would  increase  the  weight 
of  the  body. 

21.  In  all  unhealthy  countries  the  greatest  risk  of  fever  is  run  by 
sleeping  on  shore.  Is  this  owing  to  the  state  of  the  body  during  sleep, 
or  to  a greater  abundance  of  miasma  at  such  times  ? It  appears  cer- 
tain that  those  who  stay  on  board  a vessel,  though  anchored  at  only  a 
short  distance  from  the  coast,  generally  suffer  less  than  those  actually 
on  shore.  — Darwin  in  Voyage  of  Naturalist. 

22.  That  the  period  of  the  tide  should  be  accidentally  the  same  as 
that  of  the  culmination  of  the  moon,  that  the  period  of  the  highest 
tide  should  be  accidentally  the  same  as  that  of  the  syzygies,  is  possible 
in  abstracto  ; but  it  is  in  the  highest  degree  improbable  ; the  far  more 
probable  assumption  is,  either  that  sun  or  moon  produce  the  tide,  or 
that  their  motion  is  due  to  the  same  grounds  as  the  motion  of  the  tide. 

23.  In  measuring  the  velocity  of  sound  by  experiments  conducted  at 
night  with  cannon,  the  results  at  one  station  were  never  found  to  agree 
exactly  with  those  at  the  other.  Moreover,  it  was  noticed  that  on  the 
nights  when  the  discordance  was  greatest,  a strong  wind  was  blowing 
nearly  from  one  station  to  the  other. 

24.  M.  Melloni,  observing  that  the  maximum  point  of  heat  is  trans- 
ferred farther  and  farther  towards  the  red  end  of  the  spectrum,  accord- 
ing as  the  substance  of  the  prism  is  more  and  more  permeable  to  heat, 
inferred  that  a prism  of  rock  salt,  which  possesses  a greater  power 
of  transmitting  the  calorific  rays  than  any  known  body,  ought  to  throw 
the  point  of  greatest  heat  to  a considerable  distance  beyond  the  visible 
part  of  the  spectrum ; and  his  prediction  was  verified  by  subsequent 
experiment. 

25.  During  the  middle  of  the  eighteenth  century  Bonnet  and  Spal- 
lanzani discovered  that  the  horns,  tails,  legs,  eyes,  or  even  head  of 
some  creatures,  if  cut  off,  would  grow  again.  The  tail  and  legs  of  a 
salamander  were  removed  and  reproduced  themselves  eight  times  in 
succession.  By  means  of  a number  of  experiments  it  has  been  found 
that  the  more  simple  the  structure  of  an  animal  is,  the  more  do  its 
several  parts  possess  a power  of  independent  existence,  and  that  in  the 
more  complex  animals,  the  derangement  of  one  part  much  more  affects 
the  action  of  the  entire  organism. 

26.  Professor  Jevons  has  observed  that  economic  crises  have  occurred 
at  regular  intervals  of  about  ten  years.  This  ten-year  periodicity, 


420 


LOGICAL  EXERCISES 


moreover,  seems  to  correspond  to  a similar  periodicity  of  bad  harvests ; 
and  the  cause  of  this  seems  to  be  a decennial  periodicity  in  the  spots 
on  the  sun. 

27.  What  is  the  significance  of  the  remark  of  Chevreul,  the  French 
scientist : “ Every  fact  is  an  abstraction.” 

28.  Also  of  the  following  remark  of  M.  Espinas:  “If  human  activity 
was  incompatible  with  the  order  of  things,  the  act  of  boiling  an  egg 
would  have  to  be  regarded  as  a miracle.” 

29.  It  had  long  been  known  that  grasshoppers  and  crickets  have  on 
their  anterior  legs  two  peculiar,  glassy,  generally  more  or  less  oval, 
drumlike  structures  ; but  these  were  supposed  by  the  older  entomolo- 
gists to  serve  as  resonators,  and  to  reenforce  or  intensify  the  well- 
known  chirping  sounds  which  they  produce.  Johannes  Muller  was 
the  first  who  suggested  that  these  drums  or  tympana  act  like  the  tym- 
pana of  our  own  ears,  and  that  they  are  really  the  external  parts  of 
a true  auditory  apparatus.  That  any  animal  should  have  its  ears  in 
its  legs  sounds,  no  doubt,  a priori,  very  unlikely,  and  hence  probably 
the  true  function  of  this  organ  was  so  long  unsuspected. — Sir  John 
Lubbock. 

30.  In  simple  fracture  of  the  ribs,  if  the  lung  be  punctured  by  a 
fragment,  the  blood  effused  into  the  pleural  cavity,  though  freely 
mixed  with  air,  undergoes  no  decomposition.  Why  air  introduced 
into  the  pleural  cavity  through  a wounded  lung  should  have  such 
wholly  different  effects  from  that  entering  directly  through  a wound 
in  the  chest  was  to  me  a complete  mystery  until  I heard  of  the  germ- 
theory  of  putrefaction,  when  it  at  once  occurred  to  me  that  it  was  only 
natural  that  air  should  be  filtered  of  germs  by  the  air-passages,  one  of 
whose  offices  is  to  arrest  inhaled  particles  of  dust  and  prevent  them 
from  entering  the  air-cells.  — Professor  Lister. 

31.  If  the  lungs  be  emptied  as  perfectly  as  possible  and  a handful 
of  cotton-wool  be  placed  against  the  mouth  and  nostrils,  and  you 
inhale  through  it,  it  will  be  found  on  expiring  this  air  through  a glass 
tube  that  its  freedom  from  floating  matter  is  manifest.  The  applica- 
tion of  this  is  obvious  : if  a physician  wishes  to  hold  back  from  the 
lungs  of  his  patient,  or  from  his  own,  the  germs,  or  virus,  by  which 
contagious  disease  is  propagated,  he  will  employ  a cotton-wool  respi- 
rator.— Professor  Tyndall. 

32.  In  the  desert  of  North  Africa,  where  neither  trees,  brushwood, 
nor  even  undulation  of  the  surface  afford  the  slightest  protection  to 
its  foes,  a modification  of  color  in  animals  which  shall  be  assimilated 
to  that  of  the  surrounding  country  is  absolutely  necessary.  Hence, 
without  exception,  the  upper  plumage  of  every  bird,  whether  lark, 


LOGICAL  EXERCISES 


421 


chat,  sylvian,  or  sand-grouse,  and  also  the  fur  of  all  the  smaller  mam- 
mals and  the  skin  of  all  snakes  and  lizards,  is  of  one  uniform  isabelline, 
or  sand  color.  — Wallace. 

33.  Darwin,  in  investigating  the  difference  in  weight  between  cross 
and  self-fertilized  plants,  found  that  the  six  finest  crossed  plants 
averaged  108.16  ounces,  whilst  the  six  finest  self-fertilized  plants 
averaged  only  23.7  ounces,  or  as  100  to  22. 

34.  Bees  incessantly  visit  the  flowers  of  the  common  broom,  and 
these  are  adapted  by  a curious  mechanism  for  cross-fertilization. 
When  a bee  lights  on  the  wing-petals  of  a young  flower,  it  is  slightly 
opened,  and  the  short  stamens  spring  out,  which  rub  their  pollen 
against  the  abdomen  of  the  bee.  If  a rather  older  flower  is  visited 
for  the  first  time  (or  if  the  bee  exerts  great  force  on  a younger  flower), 
the  keel  opens  along  its  whole  length,  and  the  longer  as  well  as  the 
shorter  stamens,  together  with  the  much  elongated  curved  pistil, 
spring  forth  with  violence.  The  flattened  spoonlike  extremity  of 
the  pistil  rests  for  a time  on  the  back  of  the  bee,  and  leaves  on  it  the 
load  of  pollen  with  which  it  is  charged.  As  soon  as  the  bee  flies  away, 
the  pistil  instantly  curls  round,  so  that  the  stiginatic  surface  is  now 
upturned  and  occupies  a position  in  which  it  would  be  rubbed  against 
the  abdomen  of  another  bee  visiting  the  same  flower.  Thus,  when 
the  pistil  first  escapes  from  the  keel,  the  stigma  is  rubbed  against  the 
back  of  the  bee,  dusted  with  pollen  from  the  longer  stamens,  either  of 
the  same  or  another  flower  ; and  afterwards  against  the  lower  surface 
of  the  bee,  dusted  with  pollen  from  the  shorter  stamens,  which  is  often 
shed  a day  or  two  before  that  from  the  longer  stamens.  If  the  visits 
of  bees  are  prevented,  and  if  the  flowers  are  not  dashed  by  the  wind 
against  any  object,  the  keel  never  opens,  so  that  the  stamens  and 
pistil  remain  enclosed.  Plants  thus  protected  yield  very  few  pods  in 
comparison  with  those  produced  by  neighboring  uncovered  bushes, 
and  sometimes  none  at  all.  — Darwin. 

35.  Baron  Zach  received  a letter  from  Pons,  a successful  finder  of 
comets,  complaining  that  for  a certain  period  he  had  found  no  comets, 
though  he  had  sought  diligently.  Zach,  a man  of  much  sly  humor, 
told  him  that  no  spots  had  been  seen  on  the  sun  for  about  the  same 
time  — which  was  true  — and  assured  him  that  when  the  spots  came 
back,  the  comets  would  come  with  them.  Some  time  after  that  he  got 
a letter  from  Pons,  who  informed  him,  with  great  satisfaction,  that  he 
was  quite  right,  that  very  large  spots  had  appeared  on  the  sun,  and 
that  he  had  found  a fine  comet  shortly  after.  — Be  Morgan's  Budget 
of  Paradoxes. 


LOGICAL  EXERCISES 


If  Tellus  winged  be, 

The  earth  a motion  round  ; 

Then  much  deceived  are  they 
Who  nere  before  it  found. 

Solomon  was  the  wisest, 

His  wit  nere  this  attained  ; 

Cease,  then,  Copernicus, 

Thy  hypothesis  vain  ! 

— Sylvanus  Morgan , 1652. 

37.  Weather  Forecaster  Dunn  has  prepared  a chart  showing  the 
number  of  deaths  from  grip  in  New  York  City  during  the  period  from 
March  22  to  May  16,  1891,  establishing  the  relation  between  the  death- 
rates  and  weather  conditions  during  the  grip  epidemic  of  that  year. 
Mr.  Dunn  has  made  a careful  study  of  records  of  the  disease,  and 
selected  the  epidemic  of  1891  as  being  the  time  when  the  grip  was 
most  pronounced. 

He  has  apparently  demonstrated  that  the  weather  is  an  important 
factor  in  the  mortality  of  grip  cases.  He  says  that  humidity  or  mois- 
ture in  the  air  seems  to  be  the  most  important  element  in  causing  the 
disease  to  spread.  There  is  a corresponding  increase  of  deaths  with 
increasing  humidity. 

The  fatality  is  most  marked  when  the  humidity  is  at  its  maximum 
and  there  is  a sudden  fall  of  the  temperature.  This  is  shown  by  the 
record  of  April  21,  when  the  death-rate  from  grip  was  the  highest  ever 
known.  During  the  twenty-four  hours  of  that  day  250  deaths  were 
reported.  On  April  1 and  April  30  the  death-rate  was  also  high.  These 
were  days  following  a sudden  fall  in  temperature. 

All  through  the  epidemic  the  charts  show  an  increasing  death-rate 
with  high  or  increasing  humidity.  The  higher  the  humidity  and  the 
more  sudden  the  fall  in  temperature,  the  greater  was  the  number  of 
deaths.  When  the  temperature  and  the  humidity  dropped  at  the  same 
time,  there  was  a decrease  in  the  death-rate,  as  Mr.  Dunn  points  out 
by  several  examples.  He  says  that  the  lesson  to  be  learned  from  his 
chart  is  that  those  suffering  from  an  incipient  attack  of  the  grip  should 
be  most  cautious  of  the  cold,  humid  days  that  immediately  follow  the 
warm,  damp  ones. 

38.  If  in  a reservoir,  immersed  in  water,  the  air  be  compressed  to 
the  extent  of  ten  atmospheres,  and  supposing  that  now,  when  the  com- 
pressed air  has  acquired  the  temperature  of  the  water,  it  be  allowed  to 
act  upon  a piston  loaded  by  a weight,  the  weight  is  raised.  At  the 
same  time  the  water  becomes  cooler,  showing  that  a certain  quantity 


LOGICAL  EXERCISES 


423 


of  heat  had  disappeared  in  producing  the  mechanical  effort  of  raising 
the  weight. 

39.  That  the  feeling  of  effort  is  largely,  if  not  entirely,  of  peripheral 
rather  than  central  origin,  appears  from  such  experiments  as  the 
following : — 

Hold  the  finger  as  if  to  pull  the  trigger  of  a pistol.  Think  vigorously 
of  bending  the  finger,  but  do  not  bend  it.  An  unmistakable  feeling  of 
effort  results.  Repeat  the  experiment,  and  notice  that  the  breath  is 
involuntarily  held,  and  that  there  are  tensions  in  the  other  muscles. 
Repeat  the  experiment  again,  taking  care  to  keep  the  breathing  regular 
and  the  other  muscles  passive.  Little  or  no  feeling  of  effort  will  now 
accompany  the  imaginary  bending  of  the  finger.  — Ferrier. 

40.  As  to  the  nature  of  petrified  shells,  Quirini  conceived  that  as 
earthy  particles  united  in  the  sea  so  as  to  form  the  shells  of  Mollusca, 
the  same  crystallizing  process  might  be  effected  on  the  land ; and  that 
in  the  latter  case  the  germs  of  the  animals  might  have  been  dissemi- 
nated through  the  substance  of  the  rocks,  and  afterwards  developed  by 
virtue  of  humidity. 

41.  Voltaire  suggested  that  the  marine  shells  found  on  the  tops  of 
mountains  are  Eastern  species  dropped  from  the  hats  of  pilgrims  as 
they  returned  from  the  Holy  Land. 

42.  The  epicyclical  theory  of  the  heavens  was  confirmed  by  its  pre- 
dicting eclipses  of  the  sun  and  moon,  configurations  of  the  planets,  and 
other  celestial  phenomena. 

43.  Arfvedson  discovered  lithia,  by  perceiving  an  excess  of  weight 
in  the  sulphate  produced  from  a small  portion  of  what  he  considered 
as  magnesia  present  in  a mineral  he  had  analyzed. 

44.  We  see  among  the  nebula?  (which  are  diffused  along  the  Milky 
Way)  instances  of  all  degrees  of  condensation,  from  the  most  loosely 
diffused  fluid  to  that  separation  and  solidification  of  parts  by  which 
suns  and  satellites  and  planets  are  formed  ; and  thus  we  have  before 
us  instances  of  systems  in  all  their  stages,  as  in  a forest  we  see  trees 
in  every  period  of  growth.  — Laplace. 

45.  It  had  been  deductively  inferred  from  the  Copernican  theory 
that  the  planets,  Venus  and  Mercury,  ought  to  pass  through  phases, 
like  the  moon,  and  the  telescope  revealed  this  to  be  the  case. 

46.  Werner,  says  Sir  Charles  Lyell,  had  not  travelled  to  distant 
countries  ; he  had  merely  explored  a small  portion  of  Germany,  and 
conceived,  and  persuaded  others  to  believe,  that  the  whole  surface  of 
our  planet,  and  all  the  mountain  chains  in  the  world,  were  made  after 
the  model  of  his  own  province. 

47.  Scheiner  was  a monk ; and  on  communicating  to  the  superior 


424 


LOGICAL  EXERCISES 


of  his  order  the  account  of  the  spots  on  the  sun,  received  the  reply : 
“ I have  searched  through  Aristotle,  and  can  find  nothing  of  the  kind 
mentioned : be  assured,  therefore,  that  it  is  a deception  of  your  senses, 
or  of  your  glasses.” 

48.  When  we  are  told  that  a man  has  become  deranged  from 
anxiety  or  grief,  we  have  learned  very  little  if  we  rest  content  with 
that.  How  does  it  happen  that  another  man,  subjected  to  an  exactly 
similar  cause  of  grief,  does  not  go  mad  ? — Maudsley. 

49.  It  was  a general  belief  at  St.  Kilda  that  the  arrival  of  a ship 
gave  all  the  inhabitants  colds.  Dr.  John  Campbell  took  pains  to 
ascertain  the  fact  and  to  explain  it  as  the  effect  of  effluvia  arising  from 
human  bodies ; it  was  discovered,  however,  that  the  situation  of  St. 
Kilda  renders  a northeast  wind  indispensably  necessary  before  a ship 
can  make  the  landing. 

60.  Chrysippus  maintained  that  cock-fighting  was  the  final  cause  of 
cocks,  these  birds  being  made  by  Providence  in  order  to  inspire  us  by 
the  example  of  their  courage. 

61.  Touch  in  succession  various  objects  on  the  table.  A paper- 
weight, if  metallic,  is  usually  cold  to  the  touch  ; books,  paper,  and 
especially  a woollen  table-cover,  comparatively  warm.  Test  them  by 
means  of  a thermometer,  and  there  will  be  little  or  no  difference  in 
their  temperatures.  Why  then  do  some  feel  cold,  others  warm,  to  the 
touch  ? The  sense  of  touch  does  not  inform  us  directly  of  temperature, 
but  of  the  rate  at  which  our  finger  gains  or  loses  heat.  As  a rule, 
bodies  in  a room  are  colder  than  the  hand,  and  heat  always  tends  to 
pass  from  a warmer  to  a colder  body.  Of  a number  of  bodies,  all 
equally  colder  than  the  hand,  that  one  will  seem  coldest  to  the  touch, 
as  the  metallic,  which  is  able  most  rapidly  to  convey  away  heat  from 
the  hand.  — Tait. 

52.  One  of  Joule’s  experiments  concerning  the  mechanical  value  of 

light  is  as  follows  : He  compared  the  heat  evolved  in  the  wire 

conducting  a galvanic  current  when  the  wire  was  ignited  by  the 
passage  of  the  current  with  that  evolved  when  with  an  equal  current  it 
was  kept  cool  by  immersion  in  water.  These  experiments  showed  a 
small  but  unmistakable  diminution  of  the  heat  when  light  also  was 
given  out.  — Tait. 

53.  It  is  an  illusion  in  psychology  and  a corruption  of  logic  to  take 
the  conditions  which  occasion  the  logical  operations  of  thought  for  the 
operations  themselves.  There  is  only  one  delusion  more  desperate 
still,  — to  imagine  that  a complete  physical  theory  of  the  nervous 
system  will  explain  that  which  is  itself  the  condition  of  any  theory 
being  possible  at  all.  — Lutze. 


LOGICAL  EXERCISES 


425 


54.  During  the  retreat  of  the  Ten  Thousand  a cutting  north  wind 
blew  in  the  faces  of  the  soldiers  ; sacrifices  were  offered  to  Boreas,  and 
the  severity  of  the  wind  immediately  ceased,  which  seemed  a proof  of 
the  god’s  causation. 

55.  It  has  been  shown  by  observation  that  over-driven  cattle,  if 
killed  before  recovery  from  their  fatigue,  become  rigid,  and  putrefy  in 
a surprisingly  short  time.  A similar  fact  has  been  observed  in  the 
case  of  animals  hunted  to  death,  cocks  killed  during  a fight,  and 
soldiers  slain  in  battle.  The  contrary  is  remarked  when  the  muscular 
exercise  has  not  been  great  or  excessive. 

56.  A correct  analysis  of  lapis  lazuli  was  suspected  to  he  erroneous 
because  there  seemed  to  be  nothing  in  the  elements  assigned  to  it, 
which  were  silica,  alumina,  soda,  sulphur,  and  a trace  of  iron,  to 
account  for  the  brilliant  blue  color  of  the  stone. 

57.  According  to  the  theory  that  the  earth  has  but  a thin  crust,  it 
is  still  substantially  a liquid  globe,  and  therefore,  under  the  attractive 
influence  of  the  sun  and  moon,  it  ought  to  behave  like  a yielding  liquid. 
According  to  Hopkins,  Thomson,  and  others,  the  earth  in  all  its 
astronomical  relations  behaves  like  a rigid  solid,  — a solid  more  rigid 
than  a solid  globe  of  glass,  — and  the  difference  between  the  behavior 
of  a liquid  globe  and  a solid  globe  could  easily  be  detected  by  astro- 
nomical phenomena.  — Le  Conte. 

58.  Many  years  ago  I was  struck  with  the  fact  that  humblehees,  as 
a general  rule,  perforate  flowers  only  when  these  grow  in  large  num- 
bers near  together.  In  a garden  where  there  were  some  very  large 
beds  of  Stachys  coccinea  and  of  Pentstemon  argutus,  every  single 
flower  was  perforated ; but  I found  two  plants  of  the  former  species 
growing  quite  separate  with  their  petals  much  scratched,  showing  that 
they  had  been  frequently  visited  by  bees,  and  yet  not  a single  flower 
was  perforated.  I found  also  a separate  plant  of  the  Pentstemon , and 
saw  bees  entering  the  mouth  of  the  corolla  and  not  a single  flower  had 
been  perforated.  In  the  following  year  (1842)  I visited  the  same 
garden  several  times:  on  the  19th  of  July  humblehees  were  sucking 
the  flowers  in  the  proper  manner,  and  none  of  the  corollas  were  per- 
forated. On  the  7th  of  August  all  the  flowers  were  perforated,  even 
those  on  some  few  plants  of  the  salvia,  which  grew  at  a little  distance 
from  the  great  bed.  On  the  21st  of  August  only  a few  flowers  on  the 
summits  of  the  spikes  of  both  species  remained  fresh,  and  not  one  of 
these  was  now  bored.  Again,  in  my  own  garden  every  plant  in  several 
rows  of  the  common  bean  had  many  flowers  perforated;  but  I found 
three  plants  in  separate  parts  of  the  garden  which  had  sprung  up 
accidentally,  and  these  had  not  a single  flower  perforated.  General 


426 


LOGICAL  EXERCISES 


Strachey  formerly  saw  many  perforated  flowers  in  a garden  in  the 
Himalaya,  and  he  wrote  to  the  owner  to  inquire  whether  this  relation 
between  the  plants  growing  crowded  and  their  perforation  by  bees 
there  held  good,  and  was  answered  in  the  affirmative.  Hence  it  follows 
that  the  red  clover  and  the  common  bean  when  cultivated  in  great 
masses  in  fields,  Erica  tctraliz  growing  in  large  numbers  on  heaths,  — 
rows  of  the  scarlet  kidney-bean  in  the  kitchen  garden, — and  masses 
of  any  species  in  the  flower  garden  are  all  eminently  liable  to  be  per- 
forated. The  explanation  of  this  is  not  difficult.  Flowers  growing  in 
large  numbers  attract  crowds  of  insects.  They  are  thus  stimulated  to 
work  quickly  by  rivalry.  Also  many  flowers  have  their  nectaries  dry, 
which  is  most  quickly  discovered  by  biting  holes  in  them. 

— Charles  Darwin. 

69.  The  seat  of  sensation  is  in  the  heart,  as  it  is  in  the  centre  of 
the  body  ; the  brain  is  cold  in  order  that  it  may  counteract  the  heat 
of  the  heart.  In  order  to  temper  the  coldness  of  the  brain,  blood  is 
conveyed  to  the  membrane  which  envelopes  it  by  means  of  veins  or 
channels.  But,  lest  the  heat  so  conveyed  should  injure  the  brain,  the 
veins,  instead  of  being  large  and  few,  are  small  and  many,  and  the 
blood  conveyed,  instead  of  being  copious  and  thick,  is  thin  and  pure.  — 
Aristotle. 

60.  The  lungs  of  a fox  must  be  a specific  for  asthma,  because  that 
animal  is  remarkable  for  its  strong  powers  of  respiration. — Paris' 
Pharmacologia. 

61.  Galileo  discovered,  by  the  use  of  his  telescope,  the  four  small 
satellites  which  circulate  round  Jupiter.  It  was  then  inferred  that 
what  happened  on  the  smaller  scale  might  also  be  found  true  of  the 
larger  planetary  system. 

62.  The  first  step  toward  the  discovery  of  photography  was  the 
knowledge  that  visual  light  caused  a chemical  change  in  iodide  of 
silver.  The  second  step  was  to  fix  in  permanent  position  the  portion 
of  the  substance  changed  by  the  light,  while  the  unchanged  portion 
was  removed. 

From  what  is  known  of  the  chemical  elements  and  their  compounds, 
it  seems  highly  probable  that  numerous  compounds  may  exist  which 
are  sensitive  in  the  same  way  to  waves  of  entirely  different  lengths 
from  those  that  produce  vision.  Even  with  the  salts  of  silver  it  has 
long  been  known  that  the  range  of  wave-lengths  capable  of  producing 
photographic  effect  is  much  greater  than  the  visual  range  ; and  that  the 
wave-lengths  which  produce  the  maximum  physiological  effect  (light) 
are  not  the  same  as  those  that  produce  the  maximum  photographic 
effect. 


LOGICAL  EXERCISES 


427 


It  has  been  shown  by  Professor  S.  R.  Langley  that  flint  glass  is 
transparent  to  waves  about  four  times  as  long  as  the  longest  in  the 
visual  range  ; and  that  rock-salt  is  transparent  to  a range  below  the 
red  end  of  the  visible  spectrum  twenty-nine  times  as  long  as  the  entire 
visual  range.  Glass  is  opaque  to  very  short  waves,  its  limit  in  that 
direction  being  nearly  coincident  with  the  visual  limit.  Quartz,  on 
the  other  hand,  is  transparent  to  a range  of  short  waves  extending  far 
beyond  the  visual  limit,  but  is  opaque  to  very  short  waves.  May  not 
these  substances  prove  valuable  in  this  new  field  of  actinography,  as 
quartz  trains  have  proved  in  photographing  the  ultra-violet  spectrum  ? 

Should  the  report  of  this  discovery  (Rontgen’s)  be  confirmed,  we 
cannot  fail  to  accord  the  highest  praise  to  this  new  triumph  of  science, 
and  to  predict  a development  of  the  new  field  of  actinography  that 
may  prove  of  greater  importance  than  photography. 

From  the  analogy  between  this  form  of  radiant  energy  and  dark 
heat  it  might  appropriately  be  called  “dark  light.”  — The  Electrical 
World. 

63.  As  to  the  theory  of  geyser-eruption,  the  following  principles 
have  been  established.  The  boiling-point  of  water  rises  as  the  pressure 
increases,  being  293°  for  a pressure  of  four  atmospheres.  Also,  if  the 
pressure  be  diminished  when  the  water  is  under  very  strong  pressure, 
the  water  will  immediately  flash  into  steam.  Moreover,  if  the  circula- 
tion is  impeded,  as  when  the  water  is  contained  in  long,  narrow, 
irregular  tubes,  and  heated  with  great  rapidity,  the  boiling-point  will 
be  reached  below  while  it  is  far  from  this  point  in  the  upper  part  of 
the  tube.  Therefore  at  the  moment  of  eruption  the  boiling-point  for 
the  lowest  depth  is  actually  reached.  The  water  there  being  trans- 
ferred into  steam,  the  expanding  steam  would  lift  the  whole  column  of 
water  in  the  tube,  causing  an  overflow.  This  would  diminish  the  press- 
ure in  every  part  of  the  tube,  and  consequently  a large  quantity  of 
water  before  very  near  the  boiling-point  would  flash  into  steam  and 
instantly  eject  the  whole  of  the  water  in  the  pipe,  the  steam  rushing 
out  immediately  afterwards.  The  premonitory  cannonading  beneath 
is  evidently  produced  by  the  collapse  of  large  steam-bubbles  rising 
through  the  cooler  part  of  the  water  of  the  tube.  — Bunsen's  Theory. 

64.  Mackenzie’s  theory  of  geyser-eruption  is  that  the  geyser  pipe  is 
connected  by  a narrow  conduit  with  the  lower  part  of  a subterranean 
cave,  whose  walls  are  heated  by  the  near  vicinity  of  volcanic  fires. 
The  water  rising  above  the  opening  of  the  conduit,  and  changing  into 
steam,  and  having  no  way  of  escape,  would,  through  pressure  thus 
caused,  be  forced  up  the  pipe,  the  steam  rushing  after  it.  Professor 
Le  Conte  says  of  this  theory  : If  there  were  but  one  geyser,  this  would 


428 


LOGICAL  EXERCISES 


be  considered  a very  ingenious  and  probable  hypothesis  ; for  we  may 
conceive  of  a cave  and  a conduit  so  constructed  as  to  account  for  the 
phenomena.  But  there  are  so  many  geysers  that  it  is  inconceivable 
that  all  of  them  should  have  caves  and  conduits  so  peculiarly  con- 
structed. This  theory,  therefore,  is  entirely  untenable. 

65.  It  has  been  found  by  experiment  that  a current  moving  at  the 
rate  of  three  inches  per  second  will  take  up  and  carry  along  fine  clay  ; 
moving  six  inches  per  second,  will  carry  fine  sand ; eight  inches  per 
second,  coarse  sand  the  size  of  linseed ; twelve  inches,  gravel ; twenty- 
four  inches,  pebbles ; three  feet,  angular  stones  of  the  size  of  a hen’s 
egg.  It  will  be  readily  seen  that  the  carrying  power  increases  much 
more  rapidly  than  the  velocity.  For  instance,  a current  of  twelve 
inches  per  second  carries  gravel,  while  a current  of  three  feet  per 
second,  only  three  times  greater  velocity,  carries  stones  many  hundred 
times  as  large  as  grains  of  gravel. 

66.  If  wood  be  soaked  in  a strong  solution  of  sulphate  of  iron 
(copperas)  and  dried,  and  the  same  process  be  repeated  until  the 
wood  is  highly  charged  with  this  salt,  and  then  burned,  the  structure 
of  the  wood  will  be  perserved  in  the  peroxide  of  iron  left.  Also,  it  is 
well  known  that  the  smallest  fissures  and  cavities  in  rocks  are  speedily 
filled  by  infiltrating  waters  with  mineral  matters.  Now,  wood  buried 
in  soil  soaked  with  some  petrifying  material  becomes  highly  charged 
with  the  same,  and  the  cells  filled  with  infiltrated  matter,  and  when  the 
wood  decays  the  petrifying  material  is  left,  retaining  the  structure  of 
the  wood.  In  nature  also  there  is  an  additional  process,  not  illustrated 
by  the  experiment  or  by  the  example  of  infiltrated  fillings.  As  each 
particle  of  organic  matter  passes  away  by  decay,  a particle  of  mineral 
matter  takes  its  place,  until  finally  the  whole  of  the  organic  matter  is 
replaced. 

67.  As  to  the  origin  of  bitumen,  the  following  observations  have 
been  made  : Certain  organic  matters  a,t  ordinary  temperature,  in  pres- 
ence of  abundant  moisture,  and  out  of  contact  of  air,  will  undergo  a 
species  of  decomposition  or  fermentation  by  which  an  oily  or  tarry  sub- 
stance, similar  to  bitumen  is  formed.  In  the  interior  of  heaps  of  vege- 
table substance  such  bituminous  matter  is  often  found.  Fossil  cavities 
have  been  found  in  solid  limestone  containing  bitumen,  evidently 
formed  by  decomposition  of  the  animal  matter.  So,  also,  shales  have 
been  found  in  Scotland,  filled  with  fishes  which  have  changed  into 
bitumen. 

68.  Count  Rumford  in  1798  proved  that  the  common  notion  that 
heat  was  a substance  was  false,  by  boring  a large  piece  of  brass, 
under  great  pressure  of  the  borer,  whilst  the  brass  was  in  a gallon 


LOGICAL  EXERCISES 


429 


of  water ; and  at  the  end  of  two  and  one-half  hours  the  water  actually 
boiled. 

69.  Kenelm  Digby’s  treatment  of  wounds  was  to  apply  an  ointment, 
not  to  the  wound  itself,  but  to  the  sword  that  had  inflicted  it,  to  dress 
this  carefully  at  regular  intervals,  and  in  the  meantime,  having  bound 
up  the  wound,  to  leave  it  alone  for  seven  days.  It  was  observed  that 
many  cures  followed  upon  this  treatment. 

70.  When  Pascal’s  barometer  was  carried  to  the  top  of  Puy-de- 
Dome,  and  the  mercury  in  it  fell,  it  was  inferred  that  the  fall  of  the 
mercury  was  due  to  the  change  in  elevation.  Before  finally  accepting 
this  conclusion,  the  barometer  was  placed  in  exposed  positions  and  in 
sheltered,  when  the  wind  blew  and  when  it  was  calm,  in  rain  and  in 
fog ; and  these  varying  circumstances  did  not  materially  affect  the 
result. 

71.  A French  experimenter,  Pouchet,  thought  he  had  obtained 
indubitable  evidence  of  spontaneous  generation.  He  took  infusions 
of  vegetable  matter,  boiled  them  to  a pitch  sufficient  to  destroy  all 
germs  of  life,  and  hermetically  sealed  the  liquid  in  glass  flasks.  After 
an  interval,  micro-organisms  appeared.  It  seems  that  at  a certain  stage 
in  Pouchet’s  process,  he  had  occasion  to  dip  the  mouths  of  the  flasks 
in  mercury.  It  occurred  to  Pasteur,  in  repeating  the  experiments, 
that  germs  might  have  found  their  way  in  from  the  atmospheric  dust 
on  the  surface  of  this  mercury.  And  when  he  carefully  cleansed  the 
surface  of  the  mercury,  no  life  appeared  afterwards  in  his  flasks. 

72.  The  causes  to  which  the  decay  of  the  natives  of  New  Zealand 
have  been  assigned  are  given  as  follows  : drink,  disease,  European  cloth- 
ing, peace,  and  wealth.  — Journal  of  the  Anthropological  Institute. 

73.  An  eminent  judge  was  in  the  habit  of  jocosely  propounding, 
after  dinner,  a theory  that  the  cause  of  the  prevalence  of  Jacobinism  was 
the  practice  of  bearing  three  names.  He  quoted,  on  one  side,  Charles 
James  Fox,  Richard  Brinsley  Sheridan,  John  Horne  Tooke,  John 
Philpot  Curran,  Samuel  Taylor  Coleridge,  Theobald  Wolfe  Tone. 
On  the  other  hand  there  were  William  Pitt,  John  Scott,  William 
Windham,  Samuel  Horsley,  Henry  Dundas,  Edmund  Burke.  More- 
over, the  practice  of  giving  children  three  names  has  been  a growing 
practice,  and  Jacobinism  has  also  been  growing.  The  practice  of 
giving  children  three  names  is  more  common  in  America  than  in  Eng- 
land. In  England,  we  still  have  a King  and  a House  of  Lords  ; but 
the  Americans  are  Republicans.  Burke  and  Theobald  Wolfe  Tone 
are  both  Irishmen ; therefore  the  being  an  Irishman  is  not  the  cause 
of  Jacobinism.  Horsley  and  Horne  Tooke  are  both  clergymen  ; there- 
fore the  being  a clergyman  is  not  the  cause  of  Jacobinism.  Fox  and 


430 


LOGICAL  EXERCISES 


Windham  were,  both  educated  at  Oxford  ; therefore  the  being  educated 
at  Oxford  is  not  the  cause  of  Jacobinism.  Pitt  and  Horne  Tooke 
were  both  educated  at  Cambridge  ; therefore  the  being  educated  at 
Cambridge  is  not  the  cause  of  Jacobinism.  The  cause  is,  therefore, 
the  having  three  names.  — Macaulay. 

74.  The  exotic  Pelargonia  have  a peculiar  herring-bone  structure  in 
the  petals ; moreover,  the  herring-bone  structure  is  conjoined  in  the 
Pelargonia  with  the  general  characteristics  of  the  Geraniece.  Also  the 
flowers  with  such  seed-vessels  as  our  wild  geraniums  have  the  char- 
acters of  Geraniece.  It  is,  therefore,  exceedingly  probable  that  our 
wild  geraniums  should  have  the  peculiar  herring-bone  structure. 

75.  Colonies  ought  not  to  rebel  against  the  mother  country,  since 
they  are  its  children  and  children  ought  not  to  rebel  against  their 
parents. 

76.  Finding  that  the  size  of  towns  varies  concomitantly  with  the 
size  of  the  rivers  on  which  they  are  built,  an  observer  might  infer 
that  the  size  of  the  river  was  due  to  the  size  of  the  town. 

77.  An  eminent  author,  writing  on  the  work  of  the  English  Church 
before  the  Tractarian  movement,  contrasts  the  newer  state  of  things 
unfavorably  with  the  older,  because  the  Church  in  those  former  days 
taught  us  to  use  religion  as  a light  by  which  to  see  our  way  along  the 
road  of  duty.  Without  the  sun  our  eyes  would  be  of  no  use  to  us  ; but 
if  we  look  at  the  sun,  we  are  simply  dazzled  and  can  see  neither  it  nor 
anything  else.  It  is  precisely  the  same  with  theological  speculations. 
If  the  beacon  lamp  is  shining,  a man  of  healthy  mind  will  not  discuss 
the  composition  of  the  flame. 

78.  Scarlet  color  prevails  among  balsamina,  euphorbia,  pelargo- 
nium, poppy,  salvia,  bouvardia,  and  verbena,  yet  none  of  the  scarlets 
are  of  sweet  perfumes.  Some  of  the  light-colored  balsams  and  ver- 
benas are  sweet-scented,  but  none  of  the  scarlets  are.  The  common 
sage  with  blue  blooms  is  odoriferous  both  in  flower  and  foliage ; but 
the  scarlet  salvias  are  devoid  of  smell.  None  of  the  sweet-scented- 
leaved pelargoniums  have  scarlet  blooms,  and  none  of  the  scarlet 
bloomers  have  sweet  scent  of  leaves  nor  of  blooms.  Some  of  the 
white-margined  poppies  have  pleasant  odors  ; but  the  British  scarlets 
are  not  sweet-scented.  The  British  white-blooming  hawthorn  is  of 
the  most  delightful  fragrance  ; the  scarlet  flower  has  no  smell.  Some 
of  the  honeysuckles  are  sweetly  perfumed,  but  the  scarlet  trumpet  is 
scentless. 

79.  The  productive  powers  of  plants,  judging  from  the  increased 
fertility  of  the  parent  plants  and  from  the  increased  powers  of  growth 
in  the  offspring,  are  favored  by  some  degree  of  differentiation  in  the 


LOGICAL  EXERCISES 


431 


elements  which  interact  and  unite  so  as  to  form  a new  being.  Here 
we  have  some  analogy  with  chemical  affinity  or  attraction,  which 
comes  into  play  only  between  atoms  or  molecules  of  a different  nature. 
As  Professor  Miller  remarks : “ Generally  speaking,  the  greater  the 
difference  in  the  properties  of  two  bodies,  the  more  intense  is  their 
tendency  to  mutual  chemical  action.  But  between  bodies  of  a similar 
character  the  tendency  to  unite  is  feeble.” 

80.  In  affirming  that  the  growth  of  the  body  is  mechanical,  and 
that  thought,  as  exercised  by  us,  has  its  correlative  in  the  physics  of 
the  brain,  I think  the  position  of  the  “materialist”  is  stated,  as  far 
as  that  position  is  a tenable  one.  I think  the  materialist  will  be  able 
finally  to  maintain  this  position  against  all  attacks  ; but  I do  not 
think,  in  the  present  condition  of  the  human  mind,  that  he  can  pass 
beyond  this  position.  I do  not  think  he  is  entitled  to  say  that  his 
molecular  groupings  and  his  molecular  motions  explain  everything. 
In  reality,  they  explain  nothing.  The  utmost  he  can  affirm  is  the 
association  of  the  two  classes  of  phenomena,  of  whose  real  bond  of 
union  he  is  in  absolute  ignorance.  The  problem  of  the  connection  of 
body  and  soul  is  as  insoluble  in  its  modern  form  as  it  was  in  the  pre- 
scientific  ages.  Phosphorus  is  known  to  enter  into  the  composition  of 
the  human  brain,  and  a trenchant  German  writer  has  exclaimed, 
“Ohne  Phosphor,  kein  Gedanke  ! ” That  may  or  may  not  be  the 
case  ; but  even  if  we  knew  it  to  be  the  case,  the  knowledge  would  not 
lighten  our  darkness.  — Tyndall. 

81.  Granting  that  Hegel  was  more  or  less  successful  in  constructing, 
a priori,  the  leading  results  of  the  moral  sciences,  still  it  was  no  proof 
of  the  correctness  of  the  hypothesis  of  identity,  with  which  he  started. 
The  facts  of  nature  would  have  been  the  crucial  test.  That  in  the 
moral  sciences  traces  of  the  activity  of  the  human  intellect  and  of  the 
several  stages  of  its  development  should  present  themselves,  was  a 
matter  of  course  ; but  surely,  if  nature  really  reflected  the  result  of 
the  thought  of  a creative  mind,  the  system  ought,  without  difficulty,  to 
find  a place  for  her  comparatively  simple  phenomena  and  processes. 
— Helmholtz. 

82.  When  young  Galileo  was  a student  at  Pisa,  he  noticed  one  day, 
during  the  service  at  the  great  Cathedral,  the  chandelier  swinging 
backwards  and  forwards,  and  convinced  himself,  by  counting  his 
pulse,  that  the  duration  of  the  oscillations  was  independent  of  the  arc 
through  which  it  moved. 

83.  Goethe  enunciated  the  existence  of  a resemblance  between  the 
different  parts  of  one  and  the  same  organic  being.  According  to 
Goethe’s  own  account,  the  idea  first  occurred  to  him  while  looking  at 


432 


LOGICAL  EXERCISES 


a fan-palm  at  Padua.  He  was  struck  by  the  immense  variety  of 
changes  of  form  which  the  successively  developed  stem-leaves  exhibit, 
by  the  way  in  which  the  first  simple  root  leaflets  are  replaced  by  a 
series  of  more  and  more  divided  leaves,  till  we  come  to  the  most  com- 
plicated. He  afterwards  succeeded  in  discovering  the  transformation 
of  stem-leaves  into  sepals  and  petals,  and  of  sepals  and  petals  into 
stamens,  nectaries,  and  ovaries,  and  thus  he  was  led  to  the  doctrine  of 
the  metamorphosis  of  plants  which  he  published  in  1790. 

84.  A fortunate  glance  at  a broken  sheep’s-skull,  which  Goethe 
found  by  accident  on  the  sand  of  the  Lido  at  Venice,  suggested  to  him 
that  the  skull  itself  consisted  of  a series  of  very  much  altered  vertebrae. 
At  first  sight  no  two  things  can  be  more  unlike  than  the  broad,  uni- 
form, cranial  cavity  of  the  mammalia,  enclosed  by  smooth  plates,  and 
the  narrow  cylindrical  tube  of  the  spinal  marrow,  composed  of  short, 
massy,  jagged  bones.  — Helmholtz. 

85.  The  existence  of  the  so-called  blind  spot  in  the  eye  was  first 
demonstrated  by  theoretical  arguments.  While  the  long  controversy 
whether  the  perception  of  light  resided  in  the  retina  or  the  choroid 
was  still  undecided,  Mariotte  asked  himself  what  perception  there  was 
where  the  choroid  is  deficient.  He  made  experiments  to  discover  this 
point  and  in  the  course  of  them  discovered  the  blind  spot. 

86.  Haiiy  observed  that  crystals  of  “heavy  spar”  from  Sicily  and 
those  from  Derbyshire  (which  were  considered  to  be  the  same  sub- 
stance) differed  in  their  angles  of  cleavage  by  three  and  one-lialf 
degrees,  and  remarked  : “I  could  not  suppose  that  this  difference  was 
the  effect  of  any  law  of  decrement ; for  it  would  have  been  necessary 
to  suppose  so  rapid  and  complex  a law,  that  such  a hypothesis  might 
have  been  justly  regarded  as  an  abuse  of  the  theory.”  Vauquelin  by 
chemical  analysis  discovered  that  the  base  of  the  crystals  from  Sicily 
was  strontia,  and  that  of  those  from  Derbyshire  was  baryta.  These 
facts,  becoming  known  to  Haiiy,  enabled  him  by  inference  to  discover 
that  the  angles  of  crystals  might  be  employed  as  a test  for  the  presence 
of  different  substances  which  very  nearly  resemble  each  other  in  other 
respects, 

87.  Graebe,  a German  chemist,  in  investigating  a class  of  com- 
pounds, called  the  quinones,  determined  incidentally  the  molecular 
structure  of  a body  closely  resembling  alizarine,  which  had  been  dis- 
covered several  years  before.  This  body  was  derived  from  naphthaline, 
and,  like  many  similar  derivatives,  was  reduced  back  to  naphthaline 
when  heated  with  zinc-dust.  This  circumstance  led  the  chemist  to 
heat  also  madder  alizarine  with  zinc-dust,  when,  to  his  surprise,  he 
obtained  anthracene.  Of  course,  the  inference  was  at  once  drawn  that 


LOGICAL  EXEECISES 


433 


alizarine  must  have  the  same  relation  to  anthracene  that  the  allied 
coloring  matter  bore  to  naphthaline  ; and,  more  than  this,  it  was  also 
inferred  that  the  same  chemical  processes  which  produced  the  coloring 
matter  from  naphthaline  when  applied  to  anthracene  would  yield  aliza- 
rine. The  result  fully  answered  these  expectations,  and  now  alizarine 
is  manufactured  on  a large  scale  from  anthracene  obtained  from  coal- 
tar.  — Coolie , The  New  Chemistry. 

88.  Sir  Charles  Lyell,  by  studying  the  fact  that  the  river  Ganges 
yearly  conveys  to  the  ocean  as  much  earth  as  would  form  sixty  of  the 
great  pyramids  of  Egypt,  was  enabled  to  infer  that  the  ordinary  slow 
causes  now  in  operation  upon  the  earth  would  account  for  the  immense 
geological  changes  that  have  occurred,  without  having  recourse  to  the 
less  reasonable  theory  of  sudden  catastrophes. 

89.  Joule’s  experiments  show  that  when  heat  is  produced  by  the 
consumption  of  work,  a definite  quantity  of  work  is  required  to  produce 
that  amount  of  heat  which  is  known  to  the  physicists  as  the  unit  of 
heat ; the  heat,  that  is  to  say,  which  is  necessary  to  raise  one  gramme 
of  water  through  one  degree  centigrade.  The  quantity  of  work  neces- 
sary for  this  is,  according  to  Joule’s  best  experiments,  equal  to  the 
work  which  a gramme  would  perform  in  falling  through  a height  of 
425  metres. 

In  order  to  show  how  closely  concordant  are  his  numbers,  I will 
adduce  the  results  of  a few  series  of  experiments  which  he  obtained 
after  introducing  the  latest  improvements  in  his  methods. 

(а)  A series  of  experiments  in  which  water  was  heated  by  friction 
in  a brass  vessel.  In  the  interior  of  this  vessel  a vertical  axis  provided 
with  sixteen  paddles  was  rotated,  the  eddies  thus  produced  being  broken 
by  a series  of  projecting  barriers,  in  which  parts  were  cut  out  large 
enough  for  the  paddles  to  pass  through.  The  value  of  the  equivalent 
was  424.9  metres. 

(б)  Two  similar  experiments,  in  which  mercury  in  an  iron  vessel 
was  substituted  for  water  in  a brass  one,  gave  425  and  426.3  metres 
respectively. 

(c)  Two  series  of  experiments,  in  which  a conical  ring  rubbed 
against  another,  both  surrounded  by  mercury,  gave  426.7  and  425.6 
metres  respectively. 

Exactly  the  same  relations  between  heat  and  work  were  also  found 
in  the  reverse  process;  that  is,  when  work  was  produced  by  heat. — 
Helmholtz. 

90.  A gas  which  is  allowed  to  expand  with  moderate  velocity  be- 
comes cooled.  Joule  was  the  first  to  show  the  reason  of  this  cooling. 
Eor  the  gas  has,  in  expanding,  to  overcome  the  resistance  which  the 


434 


LOGICAL  EXERCISES 


pressure  of  the  atmosphere  and  the  slowly  yielding  sides  of  the  vessel 
opposed  to  it ; or,  if  it  cannot  of  itself  overcome  this  resistance,  it  sup- 
ports the  arm  of  the  observer,  which  does  it.  Gas  thus  performs  work, 
and  this  work  is  produced  at  the  cost  of  its  heat.  Hence  the  cooling. 
If,  on  the  contrary,  the  gas  is  suddenly  allowed  to  issue  into  a perfectly 
exhausted  space  where  it  finds  no  resistance,  it  does  not  become  cool, 
as  Joule  has  shown.  — Helmholtz. 

91.  The  principal  feature  in  the  plan  of  my  attempt  to  penetrate 
into  the  North  Polar  region,  or  if  possible  to  cross  it,  is,  in  brief,  to  try 
to  make  use  of  the  currents  of  the  sea,  instead  of  fighting  against  them. 
My  opinion  is,  as  I have  already  explained  on  several  occasions,  that 
there  must  somewhere  run  currents  into  the  Polar  region,  which  carry 
the  floe-ice  across  the  Polar  Sea,  first  northward  toward  the  Pole,  and 
then  southward  again  into  the  Atlantic  Ocean.  That  these  currents 
really  exist  all  Arctic  expeditions  prove,  as  most  of  them  have  had  to 
fight  against  the  currents  and  against  the  ice  drifting  southward,  be- 
cause they  have  tried  to  get  northward  from  the  wrong  side.  I think 
a very  simple  conclusion  must  be  drawn  from  this  fact  that  currents 
and  drifting  ice  are  constantly  coming  from  the  unknown  north,  viz.  : 
Currents  and  perhaps  also  ice  must  pass  into  this  same  region,  as  the 
water  running  out  must  be  replaced  by  water  running  in.  This  con- 
clusion is  based  upon  the  simplest  of  all  natural  laws  ; but  there  seem 
to  be  people  who  will  not  even  admit  the  necessity  of  this. 

That  such  currents  run  across  the  North  Polar  region  is  also  proved 
by  many  facts.  I may  mention  the  great  quantities  of  Siberian 
driftwood  which  are  annually  carried  to  the  shores  of  Spitzbergen  and 
Greenland  ; it  comes  in  such  abundance  and  with  such  regularity  that 
it  is  quite  impossible  it  should  be  carried  to  these  shores,  so  far  from 
the  original  home,  by  occasional  winds  or  currents.  There  must  be  a 
regular  communication  between  the  coasts  of  Siberia  and  those  of 
Spitzbergen  and  Greenland.  By  this  same  communication  were  several 
objects  from  the  unfortunate  Jeannette  carried  to  the  Greenland  coast. 
The  Jeannette  sank  in  June,  1881,  to  the  north  of  the  New  Siberian 
Islands,  and  three  years  afterward,  in  June,  1884,  a great  many  objects 
belonging  to  her  or  her  crew  were  found  on  an  ice-floe  on  the  southwest 
coast  of  Greenland.  This  floe  can  only  have  been  brought  there  by  the 
same  current  which  carries  the  driftwood.  By  this  same  current  an 
Esquimau  implement,  a throwing-stick  or  harpoon-thrower,  was  also 
carried  the  long  way  from  Alaska  to  the  west  coast  of  Greenland. 
There  can, in  my  opinion,  be  no  doubt  of  the  existence  of  such  a com- 
munication or  current  across  the  North  Polar  region  from  the  Siberian 
side  to  the  Greenland  side.  — Dr.  Nansen  in  The  Strand  Magazine. 


INDEX 


Abstract,  20. 

Abstraction,  15. 

Accent,  160. 

Accident,  391.,  161. 

Adams,  272. 

A dicto  secundum  quid  ad  dictum 
simpliciter,  161. 

A dicto  simpliciter  ad  dictum  secun- 
dum quid,  161. 

^Esthetics  and  logic,  11. 

Agassiz,  72. 

Agreement,  method  of,  222  f. 

Algebra  and  logic,  123. 

Ambiguity,  fallacies  of,  158  ff . 
Amphiboly,  159. 

Analogy,  151,  187,  314  f.,  371,  375. 
Analysis,  376. 
dtpaipems,  15. 

Aquapendente,  319. 

Argumentum  ad  baculum,  162; 
hominem,  162;  ignorantiam,  162; 
judicum,  163;  populum,  162;  rem, 
163 ; verecundiam,  162. 

Aristotle,  15,  23,  37,  53,  103,  104, 138, 
139,  157,  164,  169,  192,  195,  386  f., 
390. 

Bacon,  62  f.,  169,  192,  212,  213,  230, 
310,  326,  363  f.,  369,  370,  390  f. 

Bain,  169,  327. 

Barrett,  204,  360. 

Begriff,  5. 

Beneke,  185. 

Bergmann,  367. 

Berkeley,  17. 

Beudant,  267. 

Bluntschli,  383  f. 

Boole,  325. 

Bosanquet,  89,  99,  176,  177,  185,  187, 
189,  201,  219,  397. 

Boyle,  237. 


Brahe',  Tycho,  215,  390. 

Brewster,  187,  233. 

Brown,  202. 

Bullen,  346. 

Bunsen,  345. 

Caesalpinus,  390. 

Campanella,  389. 

Categorical  judgment,  78  f. 
Categories,  37. 

Causal  analysis,  188,  206  ff. 
Causation,  41,  195  ff.,  330  f. 
Chalmers,  210. 

Chemistry,  method  of,  378. 
Chenevix,  362. 

Circulus  in  definiendo,  46;  in  pro - 
bando,  165. 

Circumstantial  evidence,  346. 

Clark,  281. 

Classification,  55 f.,  316,  372,  374; 
artificial,  56 ; as  affected  by  evolu- 
tion, 59  f. ; serial,  58 ; natural,  56  f. ; 
of  the  sciences,  62  f . 

Clifford,  195,  284  f .,  290,  324. 
Coexistence,  208. 

Coincidence  and  cause,  345. 
Collective  use  of  a term,  160. 
Collocation,  209  f.,  353. 

Composition,  159. 

Comte,  62  f. 

Concept,  5,  7,  10,  13  f.,  25  f. 
Conceptual  processes,  fallacies  of, 
359. 

Concomitant  variations,  method  of, 
223,  258  ff . 

Concrete,  21. 

Concurrence,  207. 

Connotation,  42. 

Conservation  of  energy,  196. 
Consilience  of  inductions,  309. 
Content,  42. 


436 


INDEX 


Contradiction,  law  of,  98  ff. 

Contradictory,  107 ; opposition, 
100  f. ; terms,  52. 

Contrapositive,  111  f.,  116  f. 

Contrary,  106;  opposition,  100  f., 
terms,  52. 

Converse  accident,  161. 

Conversion,  110  f.,  117  f. 

Copernicus,  390. 

Copleston,  396. 

Copula,  33  f.,  73. 

Counter-dilemma,  147. 

Cuvier,  90  f. 

Darwin,  Charles,  209,  216,  245,  253, 
255  f.,  265  f.,  277,  283  f.,  291,  292, 
296  f.,  301,  304,  322,  324,  342. 

Darwin,  Francis,  277,  292. 

Darwin,  G.  H.,  244. 

Davy,  273,  315. 

Deduction,  96  f. ; and  induction, 
169  ff. 

Definition,  44  if. ; and  determinate 
reference,  68;  by  description,  47; 
for  purposes  of  identification,  48 ; 
genetic,  47;  nominal,  44;  real, 
44. 

Demonstrative  judgment,  68. 

De  Morgan,  214. 

Denotation,  42. 

Derivative  laws,  352. 

Descartes,  325. 

Determinate  reference,  68. 

Determination,  process  of,  74,  81. 

Diagnostic  property,  57. 

Dialectic  method,  53  f.,  369. 

Dichotomy,  51  f. 

Dictum  de  omni  et  nullo,  138. 

Difference,  method  of,  222  f., 
236  ff. 

Differentia,  39  f. 

Differentiation,  20;  of  concepts,  79. 

Dilemma,  145  f. 

Disjunctive  judgment,  78  ff. 

Distribution  of  terms,  124  ff. 

Distributive  use  of  a term,  160. 

Diversity,  13. 

Division,  50  f.,  160;  as  in  determi- 
nate reference,  68 ; empirical,  54 ; 
logical,  54. 

Duhamel,  178. 


Elimination  by  negation,  83, 102 ; in 
the  syllogism,  123. 

Empirical,  16,  30. 

Empirical  laws,  351  if. 

Enthymeme,  130  f. 

Enumeration,  184  f. 

Episyllogism,  132. 

Equivocation,  158  f. 

Ethics  and  logic,  11. 

Eudemus,  139. 

Exceptional  phenomena,  289. 
Experiment,  212  f. 

Explanation,  a form  of  inference, 
94. 

Extension,  42. 

Extra-syllogistic  reasoning,  149  ff. 

Fact  and  truth,  171. 

Fallacies,  deductive,  157  ff. ; induc- 
tive, 359  ff. 

Faraday,  204,  213  f.,  244,  245  , 246, 
267,  281,  286,  288,  314,  323,  364. 
Fichte,  53. 

Figure,  137  f. ; of  speech,  160. 

Fizeau,  280. 

Florens,  328. 

Forel,  246,  255. 

Form  and  matter,  172. 

Foucault,  280. 

Froude,  397. 

Fundamentum  divisionis.  50. 

Galenus,  139. 

Galileo,  164,  390. 

Generalization,  107  f. ; hasty,  371. 
Genetic  concept,  22  f. 

Genus,  39  f. 

Gide,  269,  342. 

Gilbert,  390. 

Glauber,  277. 

Gore,  216,  274,  292,  315,  319,  360, 362. 
Graber,  247. 

Graphic  representation  of  method  of 
concomitant  variations,  260. 
Green,  94,  192,  195,  201. 

Grimaldi,  310. 

Guyot,  233. 

Halley,  276,  281  f. 

Hamilton,  Sir  Rowan,  285. 

Harvey,  319,  329. 


INDEX 


437 


Hatchette,  267,  367. 

Hegel,  53,  54. 

Heraclitus,  365. 

Herschel,  202,  213,  277,  323,  369,  394. 

Hildebrand,  382. 

Holland,  323. 

Hume,  197  f. 

Huyghens,  279  f. 

Hypothesis,  291,  376  f. 

Hypothetical  judgment,  78  f. 

Identity,  13 ; in  difference,  94 ; law 
of,  98  ff. 

Idols  of  Bacon,  364  f. 

Ignoratio  elenchi,  162. 

Ignotum  per  ignotius,  46. 

Illicit  process,  129. 

Imagination,  299;  fallacies  of,  359. 

Immediate  inference,  a generaliza- 
tion of,  117  if. 

Impersonal  judgment,  67. 

Implication,  104;  in  immediate  in- 
ference, 103  f . 

Indirect  prediction,  286  ff. 

Individual  judgment,  69  f. 

Induction,  96  f. ; and  deduction, 
169  ff. ; as  reverse  process,  177 ; 
historical  sketch  of,  385 ; imper- 
fect and  perfect,  185 ; methods  of, 
222  ff . ; types  of,  183  ff . 

Inductive  hazard,  175. 

Inductive  methods  and  the  sciences, 
374  ff. 

Inducto  = deductive  method,  278  ff., 
375,  378. 

Inference,  9 f . ; a generalization  of 
immediate,  117  f. ; immediate, 
103  ff. ; mediate,  122  ff. ; nature 
of,  85  ff. ; relation  of,  to  judgment, 
95. 

Infima  species,  40, 

Insurance,  341. 

Intension,  42. 

Interpretation,  process  of,  6. 

Intuitionalism,  30. 

Inverse,  117  f. 

James,  93. 

Janet,  317,  327. 

Jebb,  387. 

Jenkin,  212  284  f. 


Jenner,  292,  327. 

Jevous,  177,  178,  179,  187,  210,  215, 
233,  246,  247  , 268  f.,  276,  281,  287, 
288,  316,  323,  397. 

Joint  method  of  agreement  and 
difference,  222  f.,  248  ff. 

Joule,  285. 

Judgment,  7 f.,  25  f. ; and  language, 
33 ; fallacies  of,  359  f . ; of  identifi- 
cation, 8;  particular,  40;  relation 
to  inference,  95;  singular,  67  f. ; 
universal,  36  f. 

Judgments  of  elaboration,  8. 
Jurisprudence,  method  of,  382. 

Kant,  53,  197. 

Karayopia,  37. 

Kepler,  310,  390,  395. 

Kirby,  306. 

Kircher,  323. 

Kirchoff,  345. 

Knies,  382. 

Ladd,  383  f. 

Language  and  thought,  23  f. 

La  Place,  276,  295. 

Lavater,  170. 

Law.  180. 

Laws  of  thought,  98  ff . 

Leffingwell,  344. 

Leibniz,  102. 

Leonardo  da  Vinci,  181,  388. 

Le  Verrier,  272. 

Linnaeus,  323. 

Lister,  324. 

Lloyd,  285. 

Locke,  169,  392,  396. 

Lockyer,  316. 

Logical  squares : — - A square,  118 ; 
E square,  119;  I square,  120; 
O square,  120. 

\6yos,  3,  23. 

Lotze,  162, 173,  176, 177, 179, 180,  192, 
201,  242,  302,  303,  397. 

Loua,  342. 

Lubbock,  220  f.,  246,  250,  254  f.,  307, 
312,  319,  320  f . 

Lyell,  264. 

Mallet,  245. 

Malthus,  324,  354. 


438 


INDEX 


Mansel,  200. 

Many  questions,  fallacy  of,  165. 
Mathematico-experimental  method, 
290. 

Matter  and  form,  172. 

Max  Muller,  24. 

Mechanical  energy,  211. 

Mental  picture  and  the  concept,  19. 
Method,  historical,  380  f. 

Methods  of  Mill,  222  ff. 

Middle,  undistributed,  126  f. 

Mill,  148  f.,  160, 169,  175, 180, 198,  199, 
200,  202,  209,  212,  218,  224,  257,  312, 
326,  353,  357,  394,  396. 

Minto,  396. 

Mnemonic  lines  of  the  syllogism,  139. 
Modality,  83  f. 

Modus  ponens,  144. 

Modus  ponendo  tollens,  145. 

Modus  tollendo  ponens,  146. 

Modus  tollens,  144. 

Molar  energy,  211. 

Mood,  133  If. 

Narrative  judgment,  67. 

Natural  kind,  57  f.,  314. 

Negation,  significant  and  non-sig- 
nificant, 75,  100,  101;  implication 
of,  76;  infinite,  77. 

Negative  determination,  217. 
Negative  judgment,  73  ff.,  82. 
Newman,  396. 

Newton,  14,  187,  193,  276,  279  f.,  294, 
310,  393. 

Non  causa  pro  causa,  165,  363. 

Non  sequitur,  164. 

Observation,  212  f. 

Obversion,  114  f.,  117  f. 

Oersted,  286. 

Owen,  322. 

Particular  affirmative,  104. 
Particular  negative,  104. 

Pasteur,  224,  282  f. 

Perception  and  inference,  86;  falla- 
cies of,  359  ff. 

Perceptive  judgment,  68. 

Per  genus  et  differentiam,  45,  47. 
Petitio  Principii,  164. 

Plateau,  246,  254. 


Plato,  53,  195,  385. 

Political  economy,  method  of,  382. 
Porphyry,  39 ; tree  of,  51  f . 

Post  hoc  ergo  propter  hoc,  165,  363. 
Potential  in  inference,  92. 

Potential  properties  in  concepts,  17. 
Predicables,  38  f. 

Predicate,  grammatical,  33  f. ; logi- 
cal, 33  f. 

Prediction,  278  ff. 

Preyer,  199. 

Priestley,  242. 

Probability,  330  ff. 

Proper  name  as  subject  of  a judg- 
ment, 69;  connotation  of,  70  f. 
Property,  39  f. 
irpbadetris,  15. 

Prosyllogism,  132. 

Psychology,  method  of,  379,  383. 

Quetelet,  337. 

Railroad  accidents,  339  f. 

Reality,  27  f.,  94,  96;  as  logical  sub- 
ject, 33  f. ; metaphysical  nature 
of,  31;  in  thought,  29. 

Reduction,  178. 

Reference,  indeterminate,  68  f. 
Reflection,  4. 

Refutation,  law  of  economy  of,  108. 
Relations,  validity  of,  in  reasoning, 
152  f. 

Residues,  method  of,  223,  271  ff. 
Richter,  367. 

Romanes,  311. 

Roscher,  382. 

Rule,  180. 

Saigey,  226,  262,  311. 

Saint-Pierre,  328. 

Savigny,  382. 

Sclileiermacher,  169. 

Schonbein,  275. 

Schopenhauer,  15. 

Scientific  analysis,  188. 

Senses,  as  source  of  knowledge,  4. 
Sequence,  206  f. 

Sidgwick,  363. 

Siemens,  281. 

Sigwart,  176,  177,  179,  194,  201,  209, 
230,  241,  290,  312,  397. 


lNl)EX  439 


Singular  judgment,  27,  67  f.,  79. 
Smith,  Adam,  363. 

Social  factor  in  judgment,  31  f. 
Socrates,  385. 

Socratic  method,  74. 

Sorites,  132. 

Species,  39  f. 

Spencer,  62  f.,  355,  376  £. 

Spinoza,  301. 

Sprengel,  320. 

Statistical  method,  376. 

Subaltern,  105. 

Subcontrary,  106. 

Subject,  grammatical,  33  f. ; logical, 
33  f. 

Sufficient  reason,  201  ; law  of,  98  ff. 
Summum  genus,  40. 

Syllogism,  122  ff . ; hypothetical, 
142  ff. ; disjunctive,  144  ff. 
Synthesis,  15,  376. 

System,  5,  79  f.,  89  f.,  154  f.,  170  ff. 

Tait,  196,  261,  275,  281,  287,  293,  309. 
Teleology,  317  f. 

Telesius,  389,  390. 

Tennyson,  93. 

Term,  35. 

Thackeray,  99. 

Theophrastus,  139. 

Thomson,  261,  275. 

Thought,  the  nature  of,  3 ff. 


Transformations,  110  ff. 

Trichotomy,  53. 

Trilemma,  148. 

Truth,  11,  171. 

Tyndall,  215,  218  f.,  235,  237,  262, 
263  f.,  283,  286,  298  f.,  323. 

Ueberweg,  89,  169,  181,  185,  190,  201, 
368,  387. 

Ultimate  laws,  352. 

Uniformity  of  nature,  173,  176,  196. 
Universal,  4;  in  inference,  93;  af- 
firmative, 104 ; judgment,  26,  79  f. ; 
negative,  104;  of  discourse,  101. 
Universe  of  discourse,  101. 

Variation,  limit  of,  19. 

Venn,  179,  200,  216,  225,  240,  243,  244, 
300,  357,  396,  397. 

Verification,  278 ff. 

Voltaire,  328. 

Von  Baer’s  law,  60. 

Waitmann,  314. 

Wallace,  304  f. 

Warrant  of  inference,  85  f. 
Wedgwood,  367. 

Whately,  200,  396. 

Whewell,  179,  281,  312,  367,  388,  395. 
Williams,  283. 

Wollaston,  362. 


D01 138027M 


